How do you simplify (6 - x ^2)^2?

Jun 29, 2017

See a solution process below:

Explanation:

This is a special form of a quadratic where:

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

Substituting:

$6$ for $a$

${x}^{2}$ for $b$ gives:

${\left(6 - b\right)}^{2} = {6}^{2} - \left(2 \cdot 6 \cdot {x}^{2}\right) + {\left({x}^{2}\right)}^{2} =$

$36 - 12 {x}^{2} + {x}^{4}$

Or, in standard polynomial form:

${x}^{4} - 12 {x}^{2} + 36$