Question

Factorise $4x^2{y}^6+16x^3{y}^2+24x^4{y}^3$

• A. $4x^2{y}^2(y^4+4x+6x^{2}y)$
• B. $4x^2(y^3+4x+6x^{2}y)$
• C. $4xy(y^3+4x+6x^{2}y)$
• D. $16x^2{y}^2(4y^3+16x+6x^{2}y)$

Answer 1

The correct option is A

$4x^2{y}^2(y^4+4x+6x^{2}y)$

Given $4x^2{y}^6+16x^3{y}^2+24x^4{y}^3$

$\Rightarrow 4(x^2{y}^6+4x^3{y}^2+6x^4{y}^3)$ ( Taking 4 as the common factor)

$\Rightarrow 4x^2(y^6+4x{y}^2+6x^2{y}^3)$ ( Taking $x^2$ as the common factor)

$\Rightarrow 4x^2{y}^2(y^4+4x+6x^{2}y)$ ( Taking $y^2$ as the common factor)

Hence $4x^2{y}^6+16x^3{y}^2+24x^4{y}^3$ can be factorised as $4x^2{y}^2(y^4+4x+6x^{2}y)$