Question
Answer
$$(x^2+x^4)^3-4x^6=x^{12}+3x^{10}+3x^8-3x^6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2+x^4)^3-4x^6& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^6+3x^8+3x^{10}+x^{12}-4x^6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^{12}+3x^{10}+3x^8-3x^6\end{aligned} $$ | |
| ① | Find $ \left(x^2+x^4\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = x^2 $ and $ B = x^4 $. $$ \left(x^2+x^4\right)^3 = \left( x^2 \right)^3+3 \cdot \left( x^2 \right)^2 \cdot x^4 + 3 \cdot x^2 \cdot \left( x^4 \right)^2+\left( x^4 \right)^3 = x^6+3x^8+3x^{10}+x^{12} $$ |
| ② | Combine like terms: $$ \color{blue}{x^6} +3x^8+3x^{10}+x^{12} \color{blue}{-4x^6} = x^{12}+3x^{10}+3x^8 \color{blue}{-3x^6} $$ |
This page was created using
Simplify polynomials calculator