Question
Answer
$$(x-5)^2-3(x-5)+3=x^2-13x+43$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-5)^2-3(x-5)+3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2-10x+25-3(x-5)+3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2-10x+25-(3x-15)+3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^2-10x+25-3x+15+3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^2-13x+43\end{aligned} $$ | |
| 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 $ \color{blue}{3} $ by $ \left( x-5\right) $ $$ \color{blue}{3} \cdot \left( x-5\right) = 3x-15 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 3x-15 \right) = -3x+15 $$ |
| ④ | Combine like terms: $$ x^2 \color{blue}{-10x} + \color{red}{25} \color{blue}{-3x} + \color{green}{15} + \color{green}{3} = x^2 \color{blue}{-13x} + \color{green}{43} $$ |
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