Answer
$$(x^2-4x+4)(x^2+4x+5)=x^4-7x^2-4x+20$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2-4x+4)(x^2+4x+5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^4-7x^2-4x+20\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2-4x+4}\right) $ by each term in $ \left( x^2+4x+5\right) $. $$ \left( \color{blue}{x^2-4x+4}\right) \cdot \left( x^2+4x+5\right) = \\ = x^4+ \cancel{4x^3}+5x^2 -\cancel{4x^3}-16x^2-20x+4x^2+16x+20 $$ |
| ② | Combine like terms: $$ x^4+ \, \color{blue}{ \cancel{4x^3}} \,+ \color{green}{5x^2} \, \color{blue}{ -\cancel{4x^3}} \, \color{orange}{-16x^2} \color{blue}{-20x} + \color{orange}{4x^2} + \color{blue}{16x} +20 = x^4 \color{orange}{-7x^2} \color{blue}{-4x} +20 $$ |
This page was created using
Simplify polynomials calculator