Question
Answer
$$(-x+0.015)(-3x+1.955)^3=27x^4-27x^3+9x^2-x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-x+0.015)(-3x+1.955)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(-x+0.015)(1-9x+27x^2-27x^3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}27x^4-27x^3+9x^2-x\end{aligned} $$ | |
| ① | Find $ \left(-3x+1\right)^3 $ in two steps. S1: Swap two terms inside bracket S2: apply formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = 1 $ and $ B = 3x $. $$ \left(-3x+1\right)^3 \xlongequal{ S1 } \left(1-3x\right)^3 = 1^3-3 \cdot 1^2 \cdot 3x + 3 \cdot 1 \cdot \left( 3x \right)^2-\left( 3x \right)^3 = 1-9x+27x^2-27x^3 $$ |
| ② | Multiply each term of $ \left( \color{blue}{-x0}\right) $ by each term in $ \left( 1-9x+27x^2-27x^3\right) $. $$ \left( \color{blue}{-x0}\right) \cdot \left( 1-9x+27x^2-27x^3\right) = -x+9x^2-27x^3+27x^400x0x^20x^3 $$ |
| ③ | Combine like terms: $$ \color{blue}{-x} + \color{red}{9x^2} \color{green}{-27x^3} +27x^40 \color{blue}{0x} \color{red}{0x^2} \color{green}{0x^3} = 27x^4 \color{green}{-27x^3} + \color{red}{9x^2} \color{blue}{-x} $$ |
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