Question
Answer
$$(3x-4)^4=81x^4-432x^3+864x^2-768x+256$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3x-4)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}81x^4-432x^3+864x^2-768x+256\end{aligned} $$ | |
| ① | $$ (3x-4)^4 = (3x-4)^2 \cdot (3x-4)^2 $$ |
| ② | Find $ \left(3x-4\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 3x } $ and $ B = \color{red}{ 4 }$. $$ \begin{aligned}\left(3x-4\right)^2 = \color{blue}{\left( 3x \right)^2} -2 \cdot 3x \cdot 4 + \color{red}{4^2} = 9x^2-24x+16\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{9x^2-24x+16}\right) $ by each term in $ \left( 9x^2-24x+16\right) $. $$ \left( \color{blue}{9x^2-24x+16}\right) \cdot \left( 9x^2-24x+16\right) = \\ = 81x^4-216x^3+144x^2-216x^3+576x^2-384x+144x^2-384x+256 $$ |
| ④ | Combine like terms: $$ 81x^4 \color{blue}{-216x^3} + \color{red}{144x^2} \color{blue}{-216x^3} + \color{green}{576x^2} \color{orange}{-384x} + \color{green}{144x^2} \color{orange}{-384x} +256 = \\ = 81x^4 \color{blue}{-432x^3} + \color{green}{864x^2} \color{orange}{-768x} +256 $$ |
This page was created using
Simplify polynomials calculator