Question
Answer
$$4(x+2)(x-2)(x+6)(x-6)=4x^4-160x^2+576$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4(x+2)(x-2)(x+6)(x-6)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(4x+8)(x-2)(x+6)(x-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(4x^2-8x+8x-16)(x+6)(x-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(4x^2-16)(x+6)(x-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(4x^3+24x^2-16x-96)(x-6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}4x^4-160x^2+576\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{4} $ by $ \left( x+2\right) $ $$ \color{blue}{4} \cdot \left( x+2\right) = 4x+8 $$ |
| ② | Multiply each term of $ \left( \color{blue}{4x+8}\right) $ by each term in $ \left( x-2\right) $. $$ \left( \color{blue}{4x+8}\right) \cdot \left( x-2\right) = 4x^2 -\cancel{8x}+ \cancel{8x}-16 $$ |
| ③ | Combine like terms: $$ 4x^2 \, \color{blue}{ -\cancel{8x}} \,+ \, \color{blue}{ \cancel{8x}} \,-16 = 4x^2-16 $$ |
| ④ | Multiply each term of $ \left( \color{blue}{4x^2-16}\right) $ by each term in $ \left( x+6\right) $. $$ \left( \color{blue}{4x^2-16}\right) \cdot \left( x+6\right) = 4x^3+24x^2-16x-96 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{4x^3+24x^2-16x-96}\right) $ by each term in $ \left( x-6\right) $. $$ \left( \color{blue}{4x^3+24x^2-16x-96}\right) \cdot \left( x-6\right) = \\ = 4x^4 -\cancel{24x^3}+ \cancel{24x^3}-144x^2-16x^2+ \cancel{96x} -\cancel{96x}+576 $$ |
| ⑥ | Combine like terms: $$ 4x^4 \, \color{blue}{ -\cancel{24x^3}} \,+ \, \color{blue}{ \cancel{24x^3}} \, \color{green}{-144x^2} \color{green}{-16x^2} + \, \color{orange}{ \cancel{96x}} \, \, \color{orange}{ -\cancel{96x}} \,+576 = 4x^4 \color{green}{-160x^2} +576 $$ |
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