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

Mathematics

1 answer:

kow [346]3 years ago

8 0

Answer:

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

Step-by-step 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,

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

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