Expand: (i) (px+2x)^3 (ii) (10.5)^3 (iii) (a/x-x/a)^3 (iv)(x/3-4)^3. Find Cube of Each of The Following. [S.Chand ICSE Class 9 Fundamentals of Mathematics Chapter 3 Exercise 3.1 Expansion and Factorisation Solution ]
(i) (px+2x)3
= (px)3 +3.(px)2.(2x) +3.(px). (2x)2 +(2x)3
= p3x3+3.(p2x2 ).2x + 3.px.4x2 +8x3
= p3x3+6p2x3+12px2+8x3 [Ans]
(ii) (10.5)3
= (10+0.5)3
=(10)3 +3.(10)2 .(0.5)+3.(10).(0.5)2+(0.5)3
= 1000+ 3 x 100 x 0.5 + 3 x 10 x 0.25 + 0.125
=1000+150 + 7.5 + 0.125
= 1157.625 [Ans]
(iii) (a/x-x/a)3
$\left(\frac{a}{x} – \frac{x}{a}\right)^3$
= $\left(\frac{a}{x}\right)^3 – 3.\left(\frac{a}{x}\right)^2\ldotp \frac{x}{a} + 3.\left(\frac{a}{x}\right)\ldotp \left(\frac{x}{a}\right)^2 – \left(\frac{x}{a}\right)^3$
= $\frac{a^3}{x^3} – 3.\frac{a^2}{x^2}\ldotp \frac{x}{a} + 3.\frac{a}{x}\ldotp \frac{x^2}{a^2} – \frac{x^3}{a^3}$
= $\frac{a^3}{x^3} – \frac{3a}{x} + \frac{3x}{a} – \frac{x^3}{a^3}$ [Ans]
(iv) (x/3-4)3
$\left(\frac{x}{3} – 4\right)^3$
= $\left(\frac{x}{3}\right)^3 – 3.\left(\frac{x}{3}\right)^2\ldotp 4 + 3.\left(\frac{x}{3}\right)\ldotp (4)^2 – \left(4\right)^3$
= $\frac{x^3}{27} – 3.\frac{x^2}{9}\ldotp 4 + 3.\frac{x}{3}\ldotp 16 – 64$
= $\frac{x^3}{27} – \frac{4x^2}{3} + 16x – 64$ [Ans]