Question
Answer
$$(x-5)^2(x-3)^2=x^4-16x^3+94x^2-240x+225$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-5)^2(x-3)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-10x+25)(x^2-6x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^4-16x^3+94x^2-240x+225\end{aligned} $$ | |
| 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 }$. $$ \begin{aligned}\left(x-5\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 5 + \color{red}{5^2} = x^2-10x+25\end{aligned} $$Find $ \left(x-3\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}{ 3 }$. $$ \begin{aligned}\left(x-3\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 3 + \color{red}{3^2} = x^2-6x+9\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^2-10x+25}\right) $ by each term in $ \left( x^2-6x+9\right) $. $$ \left( \color{blue}{x^2-10x+25}\right) \cdot \left( x^2-6x+9\right) = x^4-6x^3+9x^2-10x^3+60x^2-90x+25x^2-150x+225 $$ |
| ③ | Combine like terms: $$ x^4 \color{blue}{-6x^3} + \color{red}{9x^2} \color{blue}{-10x^3} + \color{green}{60x^2} \color{orange}{-90x} + \color{green}{25x^2} \color{orange}{-150x} +225 = \\ = x^4 \color{blue}{-16x^3} + \color{green}{94x^2} \color{orange}{-240x} +225 $$ |
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