Question

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

Answer 1

Answer:

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

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!

Answer 2

Answer:

( x - 22 ) ( - x + 4 )

Step-by-step explanation:

( a ² + b ² ) - 18 ( a ² + b ² ) - 88

To factor it

Let a ² + b ² be x.

Substitute it

x - 18 x ² - 88

use middle term and rewrite it

x + 4 x - 22 x - 88

factor out of x and 22

x (1 + 4 ) - 22 ( x + 4 )

Therefore ,

( x - 22 ) - ( x + 4 )