Mathematics: Factor the following(a²+b²)²-18(a²+b²)-88

CStep-by-step explanation:Sounds the most arguable....

Factor the following(a²+b²)²-18(a²+b²)-88

yvettegonzalez3390yg

09.06.2021

$\rm\displaystyle( {a}^{2} + {b}^{2} - 22)( {a}^{2} + {b}^{2} + 4)$

Step-by-step explanation:

we would like to factor the following:

$\rm\displaystyle ( {a}^{2} + {b}^{2} {)}^{2} - 18( {a}^{2} + {b}^{2} ) - 88$

let a²+b²=x

thus substitute:

$\rm\displaystyle x {}^{2} - 18x- 88$

rewrite the middle term as 4x-22x:

$\rm\displaystyle x^{2} + 4x - 22x - 88$

factor out x:

$\rm\displaystyle x( x^{} + 4)- 22x - 88$

factor out -22:

$\rm\displaystyle x( x^{} + 4)- 22(x + 4)$

group:

$\rm\displaystyle( x- 22)(x + 4)$

substitute back:

$\rm\displaystyle( {a}^{2} + {b}^{2} - 22)( {a}^{2} + {b}^{2} + 4)$

and we are done!

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