Question

The correct factorise form of $(x-y{)}^3-8x^3$ is _______

• A. $(x+y)(7x^2-4xy+y^2)$
• B. $=-(x+y)(7x^2-4xy+y^2)$
• C. $(x-y)(7x^2-4xy+y^2)$
• D. $-(x-y)(7x^2-4xy+y^2)$

Answer 1

The correct option is B $=-(x+y)(7x^2-4xy+y^2)$

Given expression $(x-y{)}^3-8x^3$$=(x-y{)}^3-(2x{)}^3$
Since, we have the formula,
$a^3-b^3=(a-b)(a^2+ab+b^2)$}
Substitute $a=(x-y),b=2x$ in above equation, we get
$(x-y{)}^3-(2x{)}^3$
$=\left[\right(x-y)-2x]\left[\right(x-y{)}^2+(x-y)\left(2x\right)+\left(2x{)}^2\right]$
$=-(x+y)(x^2-2xy+y^2+2x^2-2xy+4x^2)$
$=-(x+y)(7x^2-4xy+y^2)$
Therefore, the factorise of the given expression is $-(x+y)(7x^2-4xy+y^2)$

Hence, the correct option is option C.