Question
Answer
$$(8p^2+3pq-7q^2)^2=64p^4+48p^3q-103p^2q^2-42pq^3+49q^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(8p^2+3pq-7q^2)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}64p^4+48p^3q-103p^2q^2-42pq^3+49q^4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{8p^2+3pq-7q^2}\right) $ by each term in $ \left( 8p^2+3pq-7q^2\right) $. $$ \left( \color{blue}{8p^2+3pq-7q^2}\right) \cdot \left( 8p^2+3pq-7q^2\right) = \\ = 64p^4+24p^3q-56p^2q^2+24p^3q+9p^2q^2-21pq^3-56p^2q^2-21pq^3+49q^4 $$ |
| ② | Combine like terms: $$ 64p^4+ \color{blue}{24p^3q} \color{red}{-56p^2q^2} + \color{blue}{24p^3q} + \color{green}{9p^2q^2} \color{orange}{-21pq^3} \color{green}{-56p^2q^2} \color{orange}{-21pq^3} +49q^4 = \\ = 64p^4+ \color{blue}{48p^3q} \color{green}{-103p^2q^2} \color{orange}{-42pq^3} +49q^4 $$ |
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