Answer
$$11x(12x+1)(10x+1)(yx+1)=1320x^4y+242x^3y+1320x^3+11x^2y+242x^2+11x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}11x(12x+1)(10x+1)(yx+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(132x^2+11x)(10x+1)(yx+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(1320x^3+132x^2+110x^2+11x)(yx+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(1320x^3+242x^2+11x)(yx+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}1320x^4y+1320x^3+242x^3y+242x^2+11x^2y+11x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}1320x^4y+242x^3y+1320x^3+11x^2y+242x^2+11x\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{11x} $ by $ \left( 12x+1\right) $ $$ \color{blue}{11x} \cdot \left( 12x+1\right) = 132x^2+11x $$ |
| ② | Multiply each term of $ \left( \color{blue}{132x^2+11x}\right) $ by each term in $ \left( 10x+1\right) $. $$ \left( \color{blue}{132x^2+11x}\right) \cdot \left( 10x+1\right) = 1320x^3+132x^2+110x^2+11x $$ |
| ③ | Combine like terms: $$ 1320x^3+ \color{blue}{132x^2} + \color{blue}{110x^2} +11x = 1320x^3+ \color{blue}{242x^2} +11x $$ |
| ④ | Multiply each term of $ \left( \color{blue}{1320x^3+242x^2+11x}\right) $ by each term in $ \left( xy+1\right) $. $$ \left( \color{blue}{1320x^3+242x^2+11x}\right) \cdot \left( xy+1\right) = 1320x^4y+1320x^3+242x^3y+242x^2+11x^2y+11x $$ |
| ⑤ | Combine like terms: $$ 1320x^4y+242x^3y+1320x^3+11x^2y+242x^2+11x = 1320x^4y+242x^3y+1320x^3+11x^2y+242x^2+11x $$ |
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