# How do you multiply (7x-x^2)^2?

Jun 29, 2016

We could multiply this out all the way by hand.

${\left(7 x - {x}^{2}\right)}^{2}$ is the same as $\left(7 x - {x}^{2}\right) \left(7 x - {x}^{2}\right)$

And if we multiply those binomials by FOILing

$49 {x}^{2} - 7 {x}^{3} - 7 {x}^{3} + {x}^{4}$

$49 {x}^{2} - 14 {x}^{3} + {x}^{4}$

${x}^{4} - 14 {x}^{3} + 49 {x}^{2}$

And if you wanted to factor that:

${x}^{2} {\left(x - 7\right)}^{2}$

or rewrite it as

${x}^{2} \left(x - 7\right) \left(x - 7\right)$

FOILing is when you multiply the first terms of both binomials, then you multiply the first term of the first binomial and the second term of the second binomial, then the second term of the first binomial and the first term of the second binomial, then the last terms of both binomials. Just remember FOIL - First Outside Inside Last.