Question
Answer
$$(x+5)^2+(x+3)(x-3)=2x^2+10x+16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+5)^2+(x+3)(x-3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2+10x+25+(x+3)(x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2+10x+25+x^2-3x+3x-9 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^2+10x+25+x^2-9 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^2+10x+16\end{aligned} $$ | |
| ① | 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 | Multiply each term of $ \left( \color{blue}{x+3}\right) $ by each term in $ \left( x-3\right) $. $$ \left( \color{blue}{x+3}\right) \cdot \left( x-3\right) = x^2 -\cancel{3x}+ \cancel{3x}-9 $$ |
| ③ | Combine like terms: $$ x^2 \, \color{blue}{ -\cancel{3x}} \,+ \, \color{blue}{ \cancel{3x}} \,-9 = x^2-9 $$ |
| ④ | Combine like terms: $$ \color{blue}{x^2} +10x+ \color{red}{25} + \color{blue}{x^2} \color{red}{-9} = \color{blue}{2x^2} +10x+ \color{red}{16} $$ |
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