Question

What is the factored form of x2 + 4xy − 21y2?

Answer 1

`\mathrm{Factor}\:x^2+4xy-21y^2:\quad \left(x-3y\right)\left(x+7y\right)`

Explanation:

Given the expression

`x^2+4xy-21y^2`

We can write the expression by breaking it into the groups such as:

`=\left(x^2-3xy\right)+\left(7xy-21y^2\right)`

`\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2-3xy\mathrm{:\quad }x\left(x-3y\right)`

`\mathrm{Factor\:out\:}7y\mathrm{\:from\:}7xy-21y^2\mathrm{:\quad }7y\left(x-3y\right)`

`=x\left(x-3y\right)+7y\left(x-3y\right)`

`\mathrm{Factor\:out\:common\:term\:}x-3y`

`=\left(x-3y\right)\left(x+7y\right)`

Therefore,

`\mathrm{Factor}\:x^2+4xy-21y^2:\quad \left(x-3y\right)\left(x+7y\right)`