Question
Answer
$$(5x-1)^3+3(5x-1)-2=125x^3-75x^2+30x-6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5x-1)^3+3(5x-1)-2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}125x^3-75x^2+15x-1+3(5x-1)-2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}125x^3-75x^2+15x-1+15x-3-2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}125x^3-75x^2+30x-4-2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}125x^3-75x^2+30x-6\end{aligned} $$ | |
| ① | Find $ \left(5x-1\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = 5x $ and $ B = 1 $. $$ \left(5x-1\right)^3 = \left( 5x \right)^3-3 \cdot \left( 5x \right)^2 \cdot 1 + 3 \cdot 5x \cdot 1^2-1^3 = 125x^3-75x^2+15x-1 $$ |
| ② | Multiply $ \color{blue}{3} $ by $ \left( 5x-1\right) $ $$ \color{blue}{3} \cdot \left( 5x-1\right) = 15x-3 $$ |
| ③ | Combine like terms: $$ 125x^3-75x^2+ \color{blue}{15x} \color{red}{-1} + \color{blue}{15x} \color{red}{-3} = 125x^3-75x^2+ \color{blue}{30x} \color{red}{-4} $$ |
| ④ | Combine like terms: $$ 125x^3-75x^2+30x \color{blue}{-4} \color{blue}{-2} = 125x^3-75x^2+30x \color{blue}{-6} $$ |
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