Question
Answer
$$(3x+1)^2-(x+5)^2=8x^2-4x-24$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3x+1)^2-(x+5)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9x^2+6x+1-(x^2+10x+25) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}9x^2+6x+1-x^2-10x-25 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}8x^2-4x-24\end{aligned} $$ | |
| ① | Find $ \left(3x+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}{ 3x } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(3x+1\right)^2 = \color{blue}{\left( 3x \right)^2} +2 \cdot 3x \cdot 1 + \color{red}{1^2} = 9x^2+6x+1\end{aligned} $$Find $ \left(x+5\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 5 }$. $$ \begin{aligned}\left(x+5\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 5 + \color{red}{5^2} = x^2+10x+25\end{aligned} $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( x^2+10x+25 \right) = -x^2-10x-25 $$ |
| ③ | Combine like terms: $$ \color{blue}{9x^2} + \color{red}{6x} + \color{green}{1} \color{blue}{-x^2} \color{red}{-10x} \color{green}{-25} = \color{blue}{8x^2} \color{red}{-4x} \color{green}{-24} $$ |
This page was created using
Simplify polynomials calculator