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