R s aggarwal solutions mathematics class 6 Solutions for Chapter 8 algebraic expressions

Write the following using literals, numbers, and signs of basic operation:

(i) x increased by 12

(ii) y decreased by 7

(iii) The difference of a and b, when a > b

(iv) The product of x and y added to their sum

(v) One-third of x multiplied by the sum of a and b

(vi) 5 times x added to seven times y

(vii) Sum of x and the quotient of y by 5

(viii) x took away from 4

(ix) 2 less than the quotient of x by y

(x) x multiplied by itself

(xi) Twice x increased by y

(xii) Thrice x added to y squared

(xiii) x minus twice y

(xiv) x cubed less than y cubed

(xv) The quotient of x by 8 is multiplied by y

Ranjit scores 80 marks in English and x marks in Hindi. What is his total score in the two subjects?

If a = 2 and b = 3, find the value of

(i) a + b

(ii)a^{2}+a b

(iii)a b-a^{2}

(iv) 2a – 3b

(v) 5 a^{2}-2 a b

(vi)a^{3}-b^{3}

If x = 1, y = 2 and z = 5, find the value of

(i) 3x – 2y + 4z

(ii) x^{2}+y^{2}+z^{2}

(iii) 2 x^{2}-3 y^{2}+z^{2}

(iv) xy + yz -zx

(v)2 x^{2} y-5 y z+x y^{2}

(vi)x^{3}-y^{3}-z^{3}

If p = -2, q = -1 and r = 3, find the value of

\begin{array}{l} \mathbf (i){p}^{2}+\mathbf{q}^{2}-\mathbf{r}^{2} \\ \mathbf(ii){2} \mathbf{p}^{2}-\mathbf{q}^{2}+3 \mathbf{r}^{2} \\ \mathbf(iii){p}-\mathbf{q}-\mathbf{r} \\ \mathbf(iv){p}^{3}+\mathbf{q}^{3}+\mathbf{r}^{3}+\mathbf{3} \mathbf{p q r} \\ (v)3 p^{2} \mathbf{q}+5 \mathbf{p} \mathbf{q}^{2}+\mathbf{2} \mathbf{p q r} \\ \mathbf(vi){p}^{4}+\mathbf{q}^{4}-\mathbf{r}^{4} \end{array}

Write the coefficient of

(i) x in 13 x

(ii) y in – 5y

(iii) a in 6ab

(iv) z in -7xz

(v) p in – 2pqr

(vi)y^{2} \text { in } 8 x y^{2} z

(vii)\mathbf{x}^{3} \text { in } \mathbf{x}^{3}

(viii)x^{2} \text { in }-x^{2}

Write the numerical coefficient of

(i) ab

(ii) – 6bc

(iii) 7xyz

(iv)-2 x^{3} y^{2} z

Add:

(i) 3x, 7x

(ii) 7y, -9y

(iii) 2xy, 5xy, -xy

(iv) 3x, 2y

(v)2 x^{2},-3 x^{2}, 7 x^{2}

(vi) 7xyz, -5xyz, 9xyz, -8xyz

(vii)6 a^{3},-4 a^{3}, 10 a^{3},-8 a^{3}

(viii)x^{2}-a^{2},-5 x^{2}+2 a^{2},-4 x^{2}+4 a^{2}

Add the following:

(i)\begin{array}{l} x-3 y-2 z \\ 5 x+7 y-z \\ -7 x-2 y+4 z \end{array}

(ii)\begin{array}{l} \mathrm{m}^{2}-4 \mathrm{m}+5 \\ -2 \mathrm{m}^{2}+6 \mathrm{m}-6 \\ -\mathrm{m}^{2}-2 \mathrm{m}-7 \end{array}

(iii)\begin{array}{r} 2 x^{2}-3 x y+y^{2} \\ -7 x^{2}-5 x y-2 y^{2} \\ 4 x^{2}+x y-6 y^{2} \end{array}

(iv)\begin{array}{l} 4 x y-5 y z-7 z \\ -5 x y+2 y z+z x \\ -2 x y-3 y z+3 z x \end{array}

1. Add:

(i)

3a – 2b + 5c, 2a +5b – 7c, – a – b + C

(ii)

8a – 6ab + 5b, – 6a – ab – 8b, – 4a + 2ab + 3b

(iii)

2 x^{3}-3 x^{2}+7 x-8,-5 x^{3}+2 x^{2}-4 x+1,3-6 x+5 x^{2}-x^{3}

(iv)2 x^{2}-8 x y+7 y^{2}-8 x y^{2}, 2 x y^{2}+6 x y-y^{2}+3 x^{2}, 4 y^{2}-x y-x^{2}+x y^{2}

(v)

x^{3}+y^{3}-z^{3}+3 x y z,-x^{3}+y^{3}+z^{3}-6 x y z, x^{3}-y^{3}-z^{3}-8 x y z

(vi)

2+x-x^{2}+6 x^{3},-6-2 x+4 x^{2}-3 x^{3}, 2+x^{2}, 3-x^{3}+4 x-2 x^{2}

Subtract:

(i) 5x from 2x

(ii) – xy from 6xy

(iii) 3a from 5b

(iv) – 7x from 9y

(v)10 x^{2} \text { from }-7 x^{2}

(vi)\mathbf{a}^{2}-\mathbf{b}^{2} \text { from } \mathbf{b}^{2}-\mathbf{a}^{2}

Subtract:

(i) 5a + 7b – 2c from 3a – 7b + 4c

(ii) a – 2b -3c from -2a + 5b – 4c

(iii)5 x^{2}-3 x y+y^{2} \text { from } 7 x^{2}-2 x y-4 y^{2}

(iv)6 x^{3}-7 x^{2}+5 x-3 \text { from } 4-5 x+6 x^{2}-8 x^{3}

(v)x^{3}+2 x^{2} y+6 x y^{2}-y^{3} \text { from } y^{3}-3 x y^{2}-4 x^{2} y

(vi)-11 x^{2} y^{2}+7 x y-6 \text { from } 9 x^{2} y^{2}-6 x y+9

(vii)-2 a+b+6 d \text { from } 5 a-2 b-3 c

Simplify:

(i)2 p^{3}-3 p^{2}+4 p-5-6 p^{3}+2 p^{2}-8 p-2+6 p+8

(ii)2 x^{2}-x y+6 x-4 y+5 x y-4 x+6 x^{2}+3 y

(iii)x^{4}-6 x^{3}+2 x-7+7 x^{3}-x+5 x^{2}+2-x^{4}

\text { From the sum of } 3 x^{2}-5 x+2 \text { and }-5 x^{2}-8 x+6, \text { subtract } 4 x^{2}-9 x+7

\text { If } A=7 x^{2}+5 x y-9 y^{2}, B=-4 x^{2}+x y+5 y^{2} \text { and } C=4 y^{2}-3 x^{2}-6 x y \text { then show that } A+B+C=0

\text { What must be added to } 5 x^{3}-2 x^{2}+6 x+7 \text { to make the sum } x^{3}+3 x^{2}-x+1

Simplify:

a – (b -2a)

Simplify:

4x – (3y – x + 2z)

Simplify:

\left(a^{2}+b^{2}+2 a b\right)-\left(a^{2}+b^{2}-2 a b\right)

Simplify:

-3(a + b) + 4 (2a – 3b) – (2a – b)

Simplify:

-4 x^{2}+\left\{\left(2 x^{2}-3\right)-\left(4-3 x^{2}\right)\right\}

Simplify:

-2\left(x^{2}-y^{2}+x y\right)-3\left(x^{2}+y^{2}-x y\right)

Simplify:

a – {2b – {3a – (2b -3c)}}

Simplify:

-x + {5y – {x – (5y – 2x)}}

Simplify:

86 – {15x – 7(6x – 9) – 2{10x – 5(2 – 3x)}}