Question
Answer
$$(4x+8)(2x+4)^2-(8x+16)(2x^2+8x+8)=0$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4x+8)(2x+4)^2-(8x+16)(2x^2+8x+8)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(4x+8)(4x^2+16x+16)-(8x+16)(2x^2+8x+8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}16x^3+64x^2+64x+32x^2+128x+128-(16x^3+64x^2+64x+32x^2+128x+128) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}16x^3+96x^2+192x+128-(16x^3+96x^2+192x+128) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}16x^3+96x^2+192x+128-16x^3-96x^2-192x-128 \xlongequal{ } \\[1 em] & \xlongequal{ } \cancel{16x^3}+ \cancel{96x^2}+ \cancel{192x}+ \cancel{128} -\cancel{16x^3} -\cancel{96x^2} -\cancel{192x} -\cancel{128} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}0\end{aligned} $$ | |
| ① | Find $ \left(2x+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}{ 2x } $ and $ B = \color{red}{ 4 }$. $$ \begin{aligned}\left(2x+4\right)^2 = \color{blue}{\left( 2x \right)^2} +2 \cdot 2x \cdot 4 + \color{red}{4^2} = 4x^2+16x+16\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{4x+8}\right) $ by each term in $ \left( 4x^2+16x+16\right) $. $$ \left( \color{blue}{4x+8}\right) \cdot \left( 4x^2+16x+16\right) = 16x^3+64x^2+64x+32x^2+128x+128 $$Multiply each term of $ \left( \color{blue}{8x+16}\right) $ by each term in $ \left( 2x^2+8x+8\right) $. $$ \left( \color{blue}{8x+16}\right) \cdot \left( 2x^2+8x+8\right) = 16x^3+64x^2+64x+32x^2+128x+128 $$ |
| ③ | Combine like terms: $$ 16x^3+ \color{blue}{64x^2} + \color{red}{64x} + \color{blue}{32x^2} + \color{red}{128x} +128 = 16x^3+ \color{blue}{96x^2} + \color{red}{192x} +128 $$Combine like terms: $$ 16x^3+ \color{blue}{64x^2} + \color{red}{64x} + \color{blue}{32x^2} + \color{red}{128x} +128 = 16x^3+ \color{blue}{96x^2} + \color{red}{192x} +128 $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 16x^3+96x^2+192x+128 \right) = -16x^3-96x^2-192x-128 $$ |
| ⑤ | Combine like terms: $$ \, \color{blue}{ \cancel{16x^3}} \,+ \, \color{green}{ \cancel{96x^2}} \,+ \, \color{blue}{ \cancel{192x}} \,+ \, \color{green}{ \cancel{128}} \, \, \color{blue}{ -\cancel{16x^3}} \, \, \color{green}{ -\cancel{96x^2}} \, \, \color{blue}{ -\cancel{192x}} \, \, \color{green}{ -\cancel{128}} \, = \color{green}{0} $$ |
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