Question
Answer
$$(2x+5)(2x-5)+4(x-2)^2=8x^2-16x-9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x+5)(2x-5)+4(x-2)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x+5)(2x-5)+4(x^2-4x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x^2-10x+10x-25+4x^2-16x+16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4x^2-25+4x^2-16x+16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}8x^2-16x-9\end{aligned} $$ | |
| ① | Find $ \left(x-2\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}{ 2 }$. $$ \begin{aligned}\left(x-2\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 2 + \color{red}{2^2} = x^2-4x+4\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{2x+5}\right) $ by each term in $ \left( 2x-5\right) $. $$ \left( \color{blue}{2x+5}\right) \cdot \left( 2x-5\right) = 4x^2 -\cancel{10x}+ \cancel{10x}-25 $$Multiply $ \color{blue}{4} $ by $ \left( x^2-4x+4\right) $ $$ \color{blue}{4} \cdot \left( x^2-4x+4\right) = 4x^2-16x+16 $$ |
| ③ | Combine like terms: $$ 4x^2 \, \color{blue}{ -\cancel{10x}} \,+ \, \color{blue}{ \cancel{10x}} \,-25 = 4x^2-25 $$ |
| ④ | Combine like terms: $$ \color{blue}{4x^2} \color{red}{-25} + \color{blue}{4x^2} -16x+ \color{red}{16} = \color{blue}{8x^2} -16x \color{red}{-9} $$ |
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