Question
Answer
$$3x^3(2x-5y)-4x^3(2x+3y)=-2x^4-27x^3y$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3x^3(2x-5y)-4x^3(2x+3y)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6x^4-15x^3y-(8x^4+12x^3y) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6x^4-15x^3y-8x^4-12x^3y \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-2x^4-27x^3y\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3x^3} $ by $ \left( 2x-5y\right) $ $$ \color{blue}{3x^3} \cdot \left( 2x-5y\right) = 6x^4-15x^3y $$Multiply $ \color{blue}{4x^3} $ by $ \left( 2x+3y\right) $ $$ \color{blue}{4x^3} \cdot \left( 2x+3y\right) = 8x^4+12x^3y $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 8x^4+12x^3y \right) = -8x^4-12x^3y $$ |
| ③ | Combine like terms: $$ \color{blue}{6x^4} \color{red}{-15x^3y} \color{blue}{-8x^4} \color{red}{-12x^3y} = \color{blue}{-2x^4} \color{red}{-27x^3y} $$ |
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