Selina solutions concise maths class 9 icse Solutions for Chapter 4 chapter 4 expansions

Exercises in Chapter 4 chapter 4 expansions Grade 9

Exercise 4(A)

Exercise 4(B)

Exercise 4(C)

Exercise 4(D)

Exercise 4(E)

Questions in Exercise 4(A)

Find the square of:

(i) 2a+b

(ii) 3a+7b

(iii) 3a-4b

$\text { (iv) } \frac{3 a}{2 b}-\frac{2 b}{3 a}$

Use identities to evaluate:

(i) 101²

(ii) 502²

(iii) 97²

(iv) 998²

Evaluate:

$\begin{aligned} &\text { (i) }\\ &\left(\frac{7}{8} x+\frac{4}{5} y\right)^{2} \end{aligned}$

$\begin{aligned} &(\mathrm{ii})\\ &\left(\frac{2 x}{7}-\frac{7 y}{4}\right)^{2} \end{aligned}$

If a-b=7 and ab = 18; find a+b.

If 𝒂 +1/a= 𝟔 and 𝒂 ≠ 0; find:

(i) 𝒂 −1/a

(ii) 𝒂² −1/a²

12.If a2-3a+1=0 and a≠0; find:

(i) 𝒂 + 1/a

$\text { (ii) } \quad a^{2}+\frac{1}{a^{2}}$

The number x is 2 more than the number y. If the sum of the squares of x and y is 34; find the product of x and y.

The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.

Questions in Exercise 4(B)

Find the cube of:

(i) 3a-2b

(ii) 5a+3b

$\text { (iii) } \quad 2 a+\frac{1}{2 a} ;(a \neq 0)$

$\text { (iv) } \quad 3 a-\frac{1}{a} ;(a \neq 0)$

If a + 2b = 5; then show that: $a^{3}+8 b^{3}+30 a b=125$

$\text { If } a \neq 0 \text { and } a-\frac{1}{a}=4 ; \text { find: }$ $\text { (i) } a^{2}+\frac{1}{a^{2}}$ $\text { (ii) } \quad a^{4}+\frac{1}{a^{4}}$ $\text { (iii) } \quad a^{3}-\frac{1}{a^{3}}$

$\begin{aligned} &\text { If } x \neq 0 \text { and } x-\frac{1}{x}=2 ; \text { then show that: }\\ &x^{2}+\frac{1}{x^{2}}=x^{3}+\frac{1}{x^{3}}=x^{4}+\frac{1}{x^{4}} \end{aligned}$

If 2x-3y=10 and xy=16; find the value of 8x³-27y³ .

Two positive numbers x and y are such that x>y. if the difference of these numbers is 5 and their product is 24, find:

(i) Sum of these numbers.

(ii) Difference of their cubes.

(iii) Sum of their cubes.

$\text { If } 4 x^{2}+y^{2}=a \text { and } x y=b, \text { find the value of } 2 x+y$

Questions in Exercise 4(C)

Expand: $\text { (i) }\left(2 x-\frac{1}{x}\right)\left(3 x+\frac{2}{x}\right)$

$\text { (ii) }\left(3 a+\frac{2}{b}\right)\left(2 a-\frac{3}{b}\right)$

$\text { If } a+b+c=12 \text { and } a^{2}+b^{2}+c^{2}=50 ; \text { find } a b+b c+c a$

$\text { If } a^{2}+b^{2}+c^{2}=35 \text { and } a b+b c+c a=23 ; \text { find } a+b+c$

$\text { If } a+b+c=p \text { and } a b+b c+c a=q ; \text { find } a^{2}+b^{2}+c^{2}$

Questions in Exercise 4(D)

$\begin{array}{l} \text { If } x+2 y+3 z=0 \text { and } \\ x^{3}+4 y^{3}+9 z^{3}=18 x y z ; \text { evaluate; } \\ \frac{(x+2 y)^{2}}{x y}+\frac{(2 y+3 z)^{2}}{y z}+\frac{(3 z+x)^{2}}{z x} \end{array}$

$\text { In the expansion of }\left(2 x^{2}-8\right)(x-4)^{2} ; \text { find the value of: }$

(i) Coefficient of x³

(ii) Coefficient of x²

(iii) Constant term.

$\text { If } x>0 \text { and } x^{2}+\frac{1}{9 x^{2}}=\frac{25}{36}, \text { find: } x^{3}+\frac{1}{27 x^{3}}$

$\text { If } 2\left(x^{2}+1\right)=5 x, \text { find: }$ $\text { (i) } \quad x-\frac{1}{x}$ $\text { (ii) } \quad x^{3}-\frac{1}{x^{3}}$

$\text { If } a^{2}+b^{2}=34 \text { and } a b=12 ; \text { find: }$

(i) $(a+b)^{2}+5(a-b)^{2}$

(ii) $(a+b)^{2}+5(a-b)^{2}$

$\begin{aligned} &\text { If } 3 x-\frac{4}{x}=4 \text { and } x \neq 0 ; \text { find: }\\ &27 x^{3}-\frac{64}{x^{3}} \end{aligned}$

$\text { If } \quad x=\frac{1}{5-x} \text { and } x \neq 5, \text { find: } x^{3}-\frac{1}{x^{3}}$

The difference between two positive numbers is 4 and the difference between their cubes is 316. Find:

(i) their product

(ii) the sum of their squares.

Questions in Exercise 4(E)

Using suitable identity, evaluate:

(i) (104)³

(ii) (97)³

Evaluate: $\text { (i) } \frac{0.8 \times 0.8 \times 0.8+0.5 \times 0.5 \times 0.5}{0.8 \times 0.8-0.8 \times 0.5+0.5 \times 0.5}$ $\text { (ii) } \frac{1.2 \times 1.2+1.2 \times 0.3+0.3 \times 0.3}{1.2 \times 1.2 \times 1.2-0.3 \times 0.3 \times 0.3}$

$\text { If } x+5 y=10 ; \text { find the value of } x^{3}+125 y^{3}+150 x y-1000$

$\text { If } x=3+2 \sqrt{2}, \text { find: }$ $\text { (i) } \frac{1}{x}$ $\text { (ii) } x-\frac{1}{x}$ $\text { (iii) }\left(x-\frac{1}{x}\right)^{3}$ $\text { (iv) } x^{3}-\frac{1}{x^{3}}$

Prove that: $x^{2}+y^{2}+z^{2}-x y-y z-z x \text { is always positive. }$

Find:

(i) (a + b)(a + b) = (a + b)²

(ii) (a + b)(a + b)(a + b)

(iii) (a - b)(a - b)(a - b) by using the result of part (ii)