Question
Answer
$$(2x+1)^2(x+5)=4x^3+24x^2+21x+5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x+1)^2(x+5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(4x^2+4x+1)(x+5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x^3+20x^2+4x^2+20x+x+5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4x^3+24x^2+21x+5\end{aligned} $$ | |
| ① | Find $ \left(2x+1\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 2x } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(2x+1\right)^2 = \color{blue}{\left( 2x \right)^2} +2 \cdot 2x \cdot 1 + \color{red}{1^2} = 4x^2+4x+1\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{4x^2+4x+1}\right) $ by each term in $ \left( x+5\right) $. $$ \left( \color{blue}{4x^2+4x+1}\right) \cdot \left( x+5\right) = 4x^3+20x^2+4x^2+20x+x+5 $$ |
| ③ | Combine like terms: $$ 4x^3+ \color{blue}{20x^2} + \color{blue}{4x^2} + \color{red}{20x} + \color{red}{x} +5 = 4x^3+ \color{blue}{24x^2} + \color{red}{21x} +5 $$ |
This page was created using
Simplify polynomials calculator