Answer
$$(x+7)(x+7)(x+2)(x-1)=x^4+15x^3+61x^2+21x-98$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+7)(x+7)(x+2)(x-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+7x+7x+49)(x+2)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+14x+49)(x+2)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3+2x^2+14x^2+28x+49x+98)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(x^3+16x^2+77x+98)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}x^4+15x^3+61x^2+21x-98\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+7}\right) $ by each term in $ \left( x+7\right) $. $$ \left( \color{blue}{x+7}\right) \cdot \left( x+7\right) = x^2+7x+7x+49 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{7x} + \color{blue}{7x} +49 = x^2+ \color{blue}{14x} +49 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+14x+49}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{x^2+14x+49}\right) \cdot \left( x+2\right) = x^3+2x^2+14x^2+28x+49x+98 $$ |
| ④ | Combine like terms: $$ x^3+ \color{blue}{2x^2} + \color{blue}{14x^2} + \color{red}{28x} + \color{red}{49x} +98 = x^3+ \color{blue}{16x^2} + \color{red}{77x} +98 $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{x^3+16x^2+77x+98}\right) $ by each term in $ \left( x-1\right) $. $$ \left( \color{blue}{x^3+16x^2+77x+98}\right) \cdot \left( x-1\right) = x^4-x^3+16x^3-16x^2+77x^2-77x+98x-98 $$ |
| ⑥ | Combine like terms: $$ x^4 \color{blue}{-x^3} + \color{blue}{16x^3} \color{red}{-16x^2} + \color{red}{77x^2} \color{green}{-77x} + \color{green}{98x} -98 = x^4+ \color{blue}{15x^3} + \color{red}{61x^2} + \color{green}{21x} -98 $$ |
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