Question
Factorise$: (x - y)^3- 8x^3$
✓
Answer
$( x - y )^3- 8x^3$
$= ( x - y )^3 - ( 2x )^3$
$= ( x - y - 2x )[ (x - y)^2+ 2x(x - y) + (2x)^2]$
[ Using identity $(a^3- b^3) = (a - b)(a^2+ab+ b^2) ]$
$= (- x - y ) [ x^2+ y^2- 2xy + 2x^2- 2xy + 4x^2]$
$=- ( x + y ) [ 7x^2- 4xy + y^2]$
$= ( x - y )^3 - ( 2x )^3$
$= ( x - y - 2x )[ (x - y)^2+ 2x(x - y) + (2x)^2]$
[ Using identity $(a^3- b^3) = (a - b)(a^2+ab+ b^2) ]$
$= (- x - y ) [ x^2+ y^2- 2xy + 2x^2- 2xy + 4x^2]$
$=- ( x + y ) [ 7x^2- 4xy + y^2]$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Simplify : $\left(a^{-1}+b^{-1}\right) \div(a b)^{-1}$
→Factorise:
$\left(a^2-b^2\right)\left(c^2-d^2\right)-4 a b c d \quad\left[\right.$ Hint. Given Exp $\left.=(a c-b d)^2-(a d+b c)^2\right]$
→$\left(a^2-b^2\right)\left(c^2-d^2\right)-4 a b c d \quad\left[\right.$ Hint. Given Exp $\left.=(a c-b d)^2-(a d+b c)^2\right]$
Evaluate$: \tan (55^\circ - A) - \cot (35^\circ + A)$
→Without using trigonometric tables, evaluate.
$\frac{\operatorname{cosec}^2 67^{\circ}-\tan ^2 23^{\circ}}{\sec ^2 20^{\circ}-\cot ^2 70^{\circ}}$
→$\frac{\operatorname{cosec}^2 67^{\circ}-\tan ^2 23^{\circ}}{\sec ^2 20^{\circ}-\cot ^2 70^{\circ}}$
Find$: \text{AC}$
→If $a^2-3 a-1=0$ and $a \neq 0,$ find $: a^2-\frac{1}{a^2}$
→What sum of money will amount to $Rs. 27,783 $ in one and a half years at $10\%$ per annum compounded half yearly ?
→Find the distance of the following points from the origin :
B (-5, 5)
B (-5, 5)
Without using trigonometric tables, evaluate.
$\frac{\operatorname{cosec}^2 67^{\circ}-\tan ^2 23^{\circ}}{\sec ^2 20^{\circ}-\cot ^2 70^{\circ}}$
→$\frac{\operatorname{cosec}^2 67^{\circ}-\tan ^2 23^{\circ}}{\sec ^2 20^{\circ}-\cot ^2 70^{\circ}}$
In the given figure, LMN is a right triangle in which $\angle M =90^{\circ}$, P and Q are mid-points of LM and LN respectively. If $LM =9 cm, MN =12 cm$ and $LN =15 cm$, find :
(i) the perimeter of trapezium MNQP,
(ii) the area of trapezium MNQP.
→(i) the perimeter of trapezium MNQP,
(ii) the area of trapezium MNQP.