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

Apr 5, 2018

$81 - 36 {x}^{4} + 4 {x}^{8}$

#### Explanation:

${\left(9 - 2 {x}^{4}\right)}^{2}$

=$\left(9 - 2 {x}^{4}\right) \left(9 - 2 {x}^{4}\right)$

=$81 - 18 {x}^{4} - 18 {x}^{4} + 4 {x}^{8}$

=$81 - 36 {x}^{4} + 4 {x}^{8}$

Apr 5, 2018

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

#### Explanation:

Multiply/Simplify/Expand:

${\left(9 - 2 {x}^{4}\right)}^{2}$

Use the square of a difference:

${\left(a - b\right)}^{2} = {a}^{2} - 2 a b + {b}^{2}$,

where:

$a = 9$, and $b = 2 {x}^{4}$

Plug in the known values.

${\left(9 - 2 {x}^{4}\right)}^{2} = {9}^{2} - \left(2 \cdot 9 \cdot 2 {x}^{4}\right) + {\left(2 {x}^{4}\right)}^{2}$

Simplify ${9}^{2}$ to $81$.

${\left(9 - 2 {x}^{4}\right)}^{2} = 81 - \left(2 \cdot 9 \cdot 2 {x}^{4}\right) + {\left(2 {x}^{4}\right)}^{2}$

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

${\left(9 - 2 {x}^{4}\right)}^{2} = 81 - \left(2 \cdot 9 \cdot 2 {x}^{4}\right) + {2}^{2} \cdot {\left({x}^{4}\right)}^{2}$

Apply power rule: ${\left({a}^{m}\right)}^{n} = {a}^{m \cdot n}$

${\left(9 - 2 {x}^{4}\right)}^{2} = 81 - \left(2 \cdot 9 \cdot 2 {x}^{4}\right) + {2}^{2} \cdot {x}^{8}$

Simplify.

${\left(9 - 2 {x}^{4}\right)}^{2} = 81 - 36 {x}^{4} + 4 {x}^{8}$

Rearrange the equation in descending order.

${\left(9 - 2 {x}^{4}\right)}^{2} = 4 {x}^{8} - 36 {x}^{4} + 81$