Question
Answer
$$4(x-1)(x+1)-4(x-1)^2=8x-8$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4(x-1)(x+1)-4(x-1)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4(x-1)(x+1)-4(x^2-2x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(4x-4)(x+1)-(4x^2-8x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4x^2+4x-4x-4-(4x^2-8x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}4x^2-4-(4x^2-8x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}4x^2-4-4x^2+8x-4 \xlongequal{ } \\[1 em] & \xlongequal{ } \cancel{4x^2}-4 -\cancel{4x^2}+8x-4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}8x-8\end{aligned} $$ | |
| ① | Find $ \left(x-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}{ x } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(x-1\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 1 + \color{red}{1^2} = x^2-2x+1\end{aligned} $$ |
| ② | Multiply $ \color{blue}{4} $ by $ \left( x-1\right) $ $$ \color{blue}{4} \cdot \left( x-1\right) = 4x-4 $$Multiply $ \color{blue}{4} $ by $ \left( x^2-2x+1\right) $ $$ \color{blue}{4} \cdot \left( x^2-2x+1\right) = 4x^2-8x+4 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{4x-4}\right) $ by each term in $ \left( x+1\right) $. $$ \left( \color{blue}{4x-4}\right) \cdot \left( x+1\right) = 4x^2+ \cancel{4x} -\cancel{4x}-4 $$ |
| ④ | Combine like terms: $$ 4x^2+ \, \color{blue}{ \cancel{4x}} \, \, \color{blue}{ -\cancel{4x}} \,-4 = 4x^2-4 $$ |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 4x^2-8x+4 \right) = -4x^2+8x-4 $$ |
| ⑥ | Combine like terms: $$ \, \color{blue}{ \cancel{4x^2}} \, \color{green}{-4} \, \color{blue}{ -\cancel{4x^2}} \,+8x \color{green}{-4} = 8x \color{green}{-8} $$ |
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