Question
Answer
$$6(7x^3+5x^2-4x+4)-(6x^2+4x-3)=42x^3+24x^2-28x+27$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6(7x^3+5x^2-4x+4)-(6x^2+4x-3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}42x^3+30x^2-24x+24-(6x^2+4x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}42x^3+30x^2-24x+24-6x^2-4x+3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}42x^3+24x^2-28x+27\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{6} $ by $ \left( 7x^3+5x^2-4x+4\right) $ $$ \color{blue}{6} \cdot \left( 7x^3+5x^2-4x+4\right) = 42x^3+30x^2-24x+24 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 6x^2+4x-3 \right) = -6x^2-4x+3 $$ |
| ③ | Combine like terms: $$ 42x^3+ \color{blue}{30x^2} \color{red}{-24x} + \color{green}{24} \color{blue}{-6x^2} \color{red}{-4x} + \color{green}{3} = 42x^3+ \color{blue}{24x^2} \color{red}{-28x} + \color{green}{27} $$ |
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