Question
Factorize the following expressions:
$(2 x-3 y)^3+(4 z-2 x)^3+(3 y-4 z)^3$
$(2 x-3 y)^3+(4 z-2 x)^3+(3 y-4 z)^3$
✓
Answer
$(2 x-3 y)^3+(4 z-2 x)^3+(3 y-4 z)^3$
$\text { Let } 2 x-3 y=a, 4 z-2 x=b, 3 y-4 z=c$
$\therefore a+b+c=2 x-3 y+4 z-2 x+3 y-4 z=0$
$\because a+b+c=0$
$\therefore a^3+b^3+c^3=3 a b c$
$\therefore(2 x-3 y)^3+(4 z-2 x)^3+(3 y-4 z)^3$
$=3(2 x-3 y)(4 z-2 x)(3 y-4 z)$
$\text { Let } 2 x-3 y=a, 4 z-2 x=b, 3 y-4 z=c$
$\therefore a+b+c=2 x-3 y+4 z-2 x+3 y-4 z=0$
$\because a+b+c=0$
$\therefore a^3+b^3+c^3=3 a b c$
$\therefore(2 x-3 y)^3+(4 z-2 x)^3+(3 y-4 z)^3$
$=3(2 x-3 y)(4 z-2 x)(3 y-4 z)$
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
Rationalise the denominator of the following: $\frac{4}{\sqrt{11}-\sqrt{7}}$
→Factorise:
$(x+2)^3-(x-2)^3$
→$(x+2)^3-(x-2)^3$
The mean of $200$ items was $50$. Later on, it was on discovered that the two items were misread as $92$ and $8$ instead of $192$ and $88$. Find the correct mean.
→Evaluate the following using identities: $\big(\text{a}^2\text{b}-\text{b}^2\text{a}\big)^2$
→In the given figure, $O$ is the centre of a circle and $\angle A D C=130^{\circ}$. If $\angle B A C=x^{\circ}$, then find the value of $x$.
→Factorize the following expressions:
$p^3+27$
→$p^3+27$
In the if $\text{OX}=\frac{1}{2}\text{XY},\text{ PX}=\frac{1}{2}\text{XZ}$ and $OX = PX$, show that $XY = XZ.$ 
→Use suitable identity to find the product: $(x+8)(x-10)$
→Find the value of $k$, if $x-1$ is a factor of $4 x^3+3 x^2-4 x+k$.
→Evaluate: $(32)^{\frac{1}{5}}+(-7)^0+(64)^{\frac{1}{2}}$.
→