Answer:
[tex] \rm\displaystyle( {a}^{2} + {b}^{2} - 22)( {a}^{2} + {b}^{2} + 4)[/tex]
Step-by-step explanation:
we would like to factor the following:
[tex] \rm\displaystyle ( {a}^{2} + {b}^{2} {)}^{2} - 18( {a}^{2} + {b}^{2} ) - 88[/tex]
let a²+b²=x
thus substitute:
[tex] \rm\displaystyle x {}^{2} - 18x- 88[/tex]
rewrite the middle term as 4x-22x:
[tex] \rm\displaystyle x^{2} + 4x - 22x - 88[/tex]
factor out x:
[tex] \rm\displaystyle x( x^{} + 4)- 22x - 88[/tex]
factor out -22:
[tex] \rm\displaystyle x( x^{} + 4)- 22(x + 4)[/tex]
group:
[tex] \rm\displaystyle( x- 22)(x + 4)[/tex]
substitute back:
[tex] \rm\displaystyle( {a}^{2} + {b}^{2} - 22)( {a}^{2} + {b}^{2} + 4)[/tex]
and we are done!
