Question

How do you multiply `(9-2x^4)^2`?

Answer 1

`81-36x^4+4x^8`

Explanation:

`(9-2x^4)^2`

=`(9-2x^4)(9-2x^4)`

=`81-18x^4-18x^4+4x^8`

=`81-36x^4+4x^8`

Answer 2

`(9-2x^4)^2=color(blue)(4x^8-36x^4+81`

Explanation:

Multiply/Simplify/Expand:

`(9-2x^4)^2`

Use the square of a difference:

`(a-b)^2=a^2-2ab+b^2`,

where:

`a=9`, and `b=2x^4`

Plug in the known values.

`(9-2x^4)^2=9^2-(2*9*2x^4)+(2x^4)^2`

Simplify `9^2` to `81`.

`(9-2x^4)^2=81-(2*9*2x^4)+(2x^4)^2`

Apply the multiplicative distributive property: `(ab)^m=a^mb^m"`

`(9-2x^4)^2=81-(2*9*2x^4)+2^2*(x^4)^2`

Apply power rule: `(a^m)^n=a^(m*n)`

`(9-2x^4)^2=81-(2*9*2x^4)+2^2*x^8`

Simplify.

`(9-2x^4)^2=81-36x^4+4x^8`

Rearrange the equation in descending order.

`(9-2x^4)^2=4x^8-36x^4+81`