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Mice21 [21]
3 years ago
9

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

Mathematics
2 answers:
navik [9.2K]3 years ago
6 0

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!

Lubov Fominskaja [6]3 years ago
6 0

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 )

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