Ncert solutions mathematics class 7 Solutions for Chapter 12 algebraic expressions

Q1) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

(i) Subtraction of z from y.

(ii) One-half of the sum of numbers x and y.

(iii) The number z multiplied by itself.

(iv) One-fourth of the product of numbers p and q.

(v) Numbers x and y both squared and added.

(vi) Number 5 added to three times the product of numbers m and n.

(vii) Product of numbers y and z subtracted from 10.

(viii) Sum of numbers a and b subtracted from their product.

Q7) Identify like terms in the following:

a) -xy^2, -4yx^2, 8x^2 , 2xy^2 , 7y , -11x^2 , -100x , -11yx , 20x^{2y} , -6x^2 , y , 2xy , 3x

b) 10pq , 7p , 8q , -p^2q^2 , -7qp , -100q , -\ 23 , 12q^2p^2 , -5p^2 , 41 , 2405p , 78qp , 13p^2q , qp^2 , 701p^2

Q2) (i) Identify the terms and their factors in the following expressions

Show the terms and factors by tree diagrams.

(a) x – 3

(b) 1 + x + x^2

(c) y – y^3

(d) 5xy^2 + 7x^2y

(e) – ab +2b^2-3a^2

(ii) Identify terms and factors in the expressions given below:

(a) – 4x + 5

(b) – 4x + 5y

(c) 5y +3y^2

(d) xy + 2x^2y^2

(e) pq + q

(f) 1.2 ab – 2.4 b + 3.6 a

(g) \frac{3}{4}x+\frac{1}{4}

(h) 0.1p^2+0.2q^2

Q6) State whether a given pair of terms is of like or unlike terms.

(i) 1,100

(ii) -7x,\ \frac{5}{2}x

(iii) -29x,\ -29y

(iv) 14xy,\ 42yx

(v) 4m^2p,\ 4mp^2

(vi) 12xz,\ 12x^2y^2

Q5) Classify into monomials, binomials and trinomials.

(i) 4y-7z

(ii) y^2

(iii) x+y-xy

(iv) 100

(v) ab-a-b

(vi ) 5-3t

(vii) 4p^2q-4pq^2

(viii) 7mn

(ix) z^2-3z+8

(x) a^2+b^2

(xi) z^2+z

(xii) 1+x+x^2

Q3) Identify the numerical coefficients of terms (other than constants) in the following expressions:

(i) 5 – 3t^2

(ii) 1\ +\ t\ +\ t^{2\ }+\ t^3

(iii) x\ +\ 2xy\ +3y

(iv) 100m\ +\ 1000n

(v) -p^2-q^{2\ }+\ 7pq

(vi) 1.2a+0.8b

(vii) 3.14r^2

(viii) 2(l+b)

(ix) 0.1y+0.01y2

Q4) (a) Identify terms which contain x and give the coefficient of x .

(i) y^2x\ +\ y

(ii) 13y^2-8yx

(iii) x+y+2

(iv) 5+z+zx

(v) 1+x+xy

(iv) 12xy^2+25

(vii) 7x+xy^2

(b) Identify terms which contain y^2 and give the coefficient of y^2

(i) 8-xy^2

(ii) 5y^2+7x

(iii) 2x^2y-15xy^2+7y^2

Get the Algebraic expressions in the following cases using Variables, constants and Arithmetic operations.

Sum of numbers a and b subtracted from their product.

Get the Algebraic expressions in the following cases using Variables, constants and Arithmetic operations.

Product of numbers y and z subtracted from 10.

Get the Algebraic expressions in the following cases using Variables, constants and Arithmetic operations.

Subtraction of z from y.

Get the Algebraic expressions in the following cases using Variables, constants and Arithmetic operations.

One-half of the sum of numbers x and y.

Get the Algebraic expressions in the following cases using Variables, constants and Arithmetic operations.

The number z multiplied by itself.

Get the Algebraic expressions in the following cases using Variables, constants and Arithmetic operations.

One-fourth of the product of numbers p and q.

Get the Algebraic expressions in the following cases using Variables, constants and Arithmetic operations.

Numbers x and y both squared and added.

Get the Algebraic expressions in the following cases using Variables, constants and Arithmetic operations.

Number 5 added to three times the product of numbers m and n.

Identify the terms and their factors in the following expressions Show the terms and factors by tree diagrams.

x – 3

Identify the terms and their factors in the following expressions Show the terms and factors by tree diagrams.

1 + x + x2

Identify the terms and their factors in the following expressions Show the terms and factors by tree diagrams.

y – y3

Identify the terms and their factors in the following expressions Show the terms and factors by tree diagrams.

5xy2 + 7x2y

Identify the terms and their factors in the following expressions Show the terms and factors by tree diagrams.

– ab + 2b2 – 3a2

Identify terms and factors in the expressions given below:

– 4x + 5

Identify terms and factors in the expressions given below:

– 4x + 5y

Identify terms and factors in the expressions given below:

xy + 2x2y2

Identify terms and factors in the expressions given below:

¾ x + ¼

Identify terms and factors in the expressions given below:

0.1 p2 + 0.2 q2

Identify terms and factors in the expressions given below:

1.2 ab – 2.4 b + 3.6 a

Identify terms and factors in the expressions given below:

pq + q

Identify the numerical coefficients of terms (other than constants) in the following expressions:

2 (l + b)

Identify the numerical coefficients of terms (other than constants) in the following expressions:

5 – 3t2

Identify the numerical coefficients of terms (other than constants) in the following expressions:

100m + 1000n

Identify the numerical coefficients of terms (other than constants) in the following expressions:

1 + t + t2 + t3

Identify the numerical coefficients of terms (other than constants) in the following expressions:

x + 2xy + 3y

Identify the numerical coefficients of terms (other than constants) in the following expressions:

1.2 a + 0.8 b

Identify the numerical coefficients of terms (other than constants) in the following expressions:

0.1 y + 0.01 y2

Identify the numerical coefficients of terms (other than constants) in the following expressions:

3.14 r2

Identify terms which contain x and give the coefficient of x.

13y2 – 8yx

Identify terms which contain x and give the coefficient of x.

y2x + y

Identify terms which contain x and give the coefficient of x.

x + y + 2

Identify terms which contain x and give the coefficient of x.

5 + z + zx

Identify terms which contain y2 and give the coefficient of y2.

8 – xy2

Identify terms which contain x and give the coefficient of x.

1 + x + xy

Identify terms which contain x and give the coefficient of x.

7x + xy2

Identify terms which contain y2 and give the Coefficient of y2.

5y2 + 7x

Identify terms which contain y2 and give the Coefficient of y2.

2x2y – 15xy2 + 7y2

Identify terms which contain x and give the coefficient of x.

12xy2 + 25

Classify into Monomials, Binomials and Trinomials.

4p2q – 4pq2

Classify into Monomials, Binomials and Trinomials.

x + y – xy

Classify into Monomials, Binomials and Trinomials.

100

Classify into Monomials, Binomials and Trinomials.

ab – a – b

Classify into Monomials, Binomials and Trinomials.

5 – 3t

Classify into Monomials, Binomials and Trinomials.

7mn

Classify into Monomials, Binomials and Trinomials.

z2 – 3z + 8

Classify into Monomials, Binomials and Trinomials.

1 + x + x2

Classify into Monomials, Binomials and Trinomials.

a2 + b2

Classify into Monomials, Binomials and Trinomials.

z2 + z

Classify into Monomials, Binomials and Trinomials.

4y – 7z

Classify into Monomials, Binomials and Trinomials.

y2

State whether a given pair of terms is of like or unlike terms.

4m2p, 4mp2

State whether a given pair of terms is of like or unlike terms.

–7x, (5/2)x

State whether a given pair of terms is of like or unlike terms.

– 29x, – 29y

State whether a given pair of terms is of like or unlike terms.

1, 100

State whether a given pair of terms is of like or unlike terms.

14xy, 42yx

Identify like terms in the following:

– xy2, – 4yx2, 8×2, 2xy2, 7y, – 11×2, – 100x, – 11yx, 20x2y, – 6×2, y, 2xy, 3x

Identify like terms in the following:

10pq, 7p, 8q, – p2q2, – 7qp, – 100q, – 23, 12q2p2, – 5p2, 41, 2405p, 78qp,

13p2q, qp2, 701p2

Q2) Add:

i) 3mn,-5mn,8mn,-4mn

ii) t-8tz,3tz-z,z-t

iii) -7mn+5,12mn+2,9mn-8,-2mn-3

iv) a+b-3,b-a+3,a-b+3

v) 14x+10y-12xy-13,18-7x-10y+8xy,4xy

vi) 5m-7n,3n-4m+2,2m-3mn-5

vii) 4x^2y,-3xy^2,-5xy^2,5x^2y

viii) 3p^2q^2-4pq+5,-10p^2q^2,15+9pq+7p^2q^2

ix) ab-4a,4b-ab,4a-4b

x) x^2-y^2-1,y^2-1-x^2,1-x^2-y^2

Q3) Subtract

i) -5y^2\ from\ y^2

ii) 6xy\ from-12xy

iii) (a-b)\ from\ (a+b)

iv) a(b-5)\ from\ b(5-a)

v) -m^2+5mn\ from\ 4m^2-3mn+8

vi) -x^2+10x-5\ from\ 5x-10

vii) 5a^2-7ab+5b^{2\ }from\ 3ab-2a^2-2b^2

viii) 4pq-5q^2-3p^2\ from\ 5p^2+3q^2-pq

Q4) (a) What should be added to x^2+xy+y^2 to obtain 2x^2+3xy ?

(b) What should be subtracted from 2a+8b+10 to get -3a+7b+16

Q5) What should be taken away from 3x^2-4y^2+5xy+20 to obtain -x^2-y^2+6xy+20 ?

Q6) (a) From the sum of 3x-y+11 and -y-11 subtract 3x-y-11.

(b) From the sum of 4+3x and 5-4x+2x^2 subtract the sum of 3x^2-5x and -x^2+2x+5.

Q1) Simplify combining like terms:

i) 21b-32+7b-20b

ii) -z^2+13z^2-5z+7z^3-15z

iii) p-(p-q)-q-(q-p)

iv) 3a-2b-ab-(a-b+ab)+3ab+b-a

v) 5x^2y-5x^2+3yx^2-3y^2+x^2-y^2+8xy^2-3y^2

vi) (3y2+5y-4)-(8y-y2-4)

Simplify combining like terms:

– z2 + 13z2 – 5z + 7z3 – 15z

Simplify combining like terms:

21b – 32 + 7b – 20b

Simplify combining like terms:

p – (p – q) – q – (q – p)

Simplify combining like terms:

3a – 2b – ab – (a – b + ab) + 3ab + b – a

Simplify combining like terms:

5x2y – 5×2 + 3yx2 – 3y2 + x2 – y2 + 8xy2 – 3y2

Simplify combining like terms:

(3y2 + 5y – 4) – (8y – y2 – 4)

Add:

5m – 7n, 3n – 4m + 2, 2m – 3mn – 5

Add:

t – 8tz, 3tz – z, z – t

Add:

– 7mn + 5, 12mn + 2, 9mn – 8, – 2mn – 3

Add:

3mn, – 5mn, 8mn, – 4mn

Add:

a + b – 3, b – a + 3, a – b + 3

Add:

ab – 4a, 4b – ab, 4a – 4b

Add:

14x + 10y – 12xy – 13, 18 – 7x – 10y + 8xy, 4xy

Add:

3p2q2 – 4pq + 5, – 10 p2q2, 15 + 9pq + 7p2q2

Add:

x2 – y2 – 1, y2 – 1 – x2, 1 – x2 – y2

Add:

4x2y, – 3xy2, –5xy2, 5x2y

Subtract:

–m2 + 5mn from 4m2 – 3mn + 8

Subtract:

a (b – 5) from b (5 – a)

Subtract:

– x2 + 10x – 5 from 5x – 10

Subtract:

5a2 – 7ab + 5b2 from 3ab – 2a2 – 2b2

Subtract:

4pq – 5q2 – 3p2 from 5p2 + 3q2 – pq

Subtract :

6xy from –12xy

Subtract:

–5y2 from y2

Subtract:

(a – b) from (a + b)

What should be added to x2 + xy + y2 to obtain 2×2 + 3xy?

What should be subtracted from 2a + 8b + 10 to get – 3a + 7b + 16?

What should be taken away from 3×2 – 4y2 + 5xy + 20 to obtain – x2 – y2 + 6xy + 20?

From the sum of 3x – y + 11 and – y – 11, subtract 3x – y – 11

From the sum of 4 + 3x and 5 – 4x + 2×2, subtract the sum of 3×2 – 5x and –x2 + 2x + 5

Q3) Find the value of the following expressions, when x=-1

i) 2x-1

ii) -x+2

iii) x^2\ +\ 2x\ +\ 1

iv) 2x^2\ -\ x-2

Q5) When a\ =\ 0, b\ =\ -1 find the value of the given expressions:

i) 2a\ +\ 2b

ii) 2a^2+b^2+1

iii) 2a^2b+2ab^2+ab

iv) a^2+ab+2

Q6) Simplify the expressions and find the value if x is equal to 2

i) x+7+4(x-5)

ii) 3(x+2)+5x-7

iii) 6x+5(x-2)

iv) 4(2x-1)+3x+11

Q7) Simplify these expressions and find their values if x\ =\ 3, a\ =\ -1, b\ =\ -2

i) 3x\ -\ 5\ -\ x\ +9

ii) 2-8x+4x+4

iii) 3a\ +\ 5\ -\ 8a\ +1

iv) 10\ -\ 3b\ -\ 4\ -\ 5b

v) 2a\ -\ 2b\ -4\ -5\ +a

Q8) (i) If z = 10, find the value of z^3-3(z-10).

(ii) If p = – 10, find the value of p^2-2p-100

Q9) What should be the value of ‘a’ if the value of 2x^2+x-a\ =\ 5 equals to 5, when x = 0 ?

Q10) Simplify the expression and find its value when a=5 and b=-3

2(a^2+ab)+3-ab

Q4) If a\ =2 and b\ =\ -\ 2 find the value of

i) a^2\ +\ b^2

ii) a^2\ +\ ab\ +b^2

iii) a^{2\ }-\ b^2

Q1) If m\ =\ 2 , find the value of:

i) m-2

ii) 3m\ -\ 5

iii) 9-5m

iv) 3m^2-\ 2m\ -\ 7

v) \frac{5m}{2}-\ 4

Q2) If p\ =\ -\ 2 , find the value of:

i) 4p\ +\ 7

ii) -3p^2\ +\ 4p\ +\ 7

iii) -2p^3\ -\ 3p^2\ +\ 4p\ +7

If m = 2, find the Value of:

9 – 5m

If m = 2, find the value of:

m – 2

If m = 2, find the Value of:

3m – 5

If m = 2, find the Value of:

3m2 – 2m – 7

If m = 2, find the Value of:

(5m/2) – 4

If p = – 2, find the Value of:

– 3p2 + 4p + 7

If p = – 2, find the Value of:

– 2p3 – 3p2 + 4p + 7

If p = – 2, find the Value of:

4p + 7

Find the value of the following Expressions, when x = –1:

2×2 – x – 2

Find the value of the following Expressions, when x = –1:

2x – 7

Find the value of the following Expressions, when x = –1:

– x + 2

Find the value of the following Expressions, when x = –1:

x2 + 2x + 1

If a = 2, b = – 2, find the Value of:

a2 + ab + b2

If a = 2, b = – 2, find the Value of:

a2 – b2

If a = 2, b = – 2, find the Value of:

a2 + b2

When a = 0, b = – 1, find the value of the given Expressions:

a2 + ab + 2

When a = 0, b = – 1, find the value of the given Expressions:

2a2b + 2ab2 + ab

When a = 0, b = – 1, find the value of the given Expressions:

2a + 2b

When a = 0, b = – 1, find the value of the given Expressions:

2a2 + b2 + 1

Simplify the Expressions and find the Value if x is Equal to 2

x + 7 + 4 (x – 5)

Simplify the Expressions and find the Value if x is Equal to 2

3 (x + 2) + 5x – 7

Simplify the Expressions and find the Value if x is Equal to 2

6x + 5 (x – 2)

Simplify the Expressions and find the Value if x is Equal to 2

4(2x – 1) + 3x + 11

Simplify these Expressions and Find their Values if x = 3, a = – 1, b = – 2.

2 – 8x + 4x + 4

Simplify these Expressions and Find their Values if x = 3, a = – 1, b = – 2.

10 – 3b – 4 – 5b

Simplify these Expressions and Find their Values if x = 3, a = – 1, b = – 2

2a – 2b – 4 – 5 + a

Simplify these Expressions and Find their Values if x = 3, a = – 1, b = – 2.

3a + 5 – 8a + 1

Simplify these Expressions and Find their Values if x = 3, a = – 1, b = – 2.

3x – 5 – x + 9

If p = – 10, find the value of p2 – 2p – 100

If z = 10, find the value of z3 – 3(z – 10)

What should be the value of a if the value of 2×2 + x – a equals to 5, when x = 0?

Simplify the Expression and Find its Value when a = 5 and b = – 3.

2(a2 + ab) + 3 – ab

Q2) Use the given algebraic expression to complete the table of number patterns.

Q1) Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.

If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern. How many segments are required to form 5, 10, 100 digits of the kind 6, 4, 3.

Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.

If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern. How many segments are required to form 5, 10, 100 digits of the kind

Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.

If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern. How many segments are required to form 5, 10, 100 digits of the kind

Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.

If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern. How many segments are required to form 5, 10, 100 digits of the kind

Use the given Algebraic Expression to Complete the Table of Number Patterns.

Use the given Algebraic Expression to Complete the Table of Number Patterns.

Use the given Algebraic Expression to Complete the Table of Number Patterns.

Use the given Algebraic Expression to Complete the Table of Number Patterns.