Question
Answer
$$15(x-5)\cdot3(x-5)(5x+1)=225x^3-2205x^2+5175x+1125$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}15(x-5)\cdot3(x-5)(5x+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(15x-75)\cdot3(x-5)(5x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(45x-225)(x-5)(5x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(45x^2-225x-225x+1125)(5x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(45x^2-450x+1125)(5x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}225x^3+45x^2-2250x^2-450x+5625x+1125 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}225x^3-2205x^2+5175x+1125\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{15} $ by $ \left( x-5\right) $ $$ \color{blue}{15} \cdot \left( x-5\right) = 15x-75 $$ |
| ② | $$ \left( \color{blue}{15x-75}\right) \cdot 3 = 45x-225 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{45x-225}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{45x-225}\right) \cdot \left( x-5\right) = 45x^2-225x-225x+1125 $$ |
| ④ | Combine like terms: $$ 45x^2 \color{blue}{-225x} \color{blue}{-225x} +1125 = 45x^2 \color{blue}{-450x} +1125 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{45x^2-450x+1125}\right) $ by each term in $ \left( 5x+1\right) $. $$ \left( \color{blue}{45x^2-450x+1125}\right) \cdot \left( 5x+1\right) = 225x^3+45x^2-2250x^2-450x+5625x+1125 $$ |
| ⑥ | Combine like terms: $$ 225x^3+ \color{blue}{45x^2} \color{blue}{-2250x^2} \color{red}{-450x} + \color{red}{5625x} +1125 = 225x^3 \color{blue}{-2205x^2} + \color{red}{5175x} +1125 $$ |
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