Question

How do you factor completely: `81x^4 - 16`?

Answer 1

`=color(red)((9x^2+4)(3x+2)(3x-2))`

Explanation:

-As per the identity:

`color(blue)((a^2-b^2) = (a+b)(a-b)`

Here :
`color(blue)(9x^2) = a`
`color(blue)(4) =b`

Applying the identity to the expression:
`81x^4 - 16 =color(blue)( (9x^2)^2 - 4^2`

`=color(blue)((9x^2+4))color(green)((9x^2-4)`

`9x^2-4` can be factorised further using the same identity

`9x^2-4 = (3x)^2 - 2^2 = color(green)((3x+2)(3x-2)`

`81x^4 - 16 =color(red)((9x^2+4)(3x+2)(3x-2))`