Answer
$$x(x+2)(x+4)(x+6)=x^4+12x^3+44x^2+48x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x(x+2)(x+4)(x+6)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+2x)(x+4)(x+6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^3+4x^2+2x^2+8x)(x+6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3+6x^2+8x)(x+6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^4+6x^3+6x^3+36x^2+8x^2+48x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}x^4+12x^3+44x^2+48x\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{x} $ by $ \left( x+2\right) $ $$ \color{blue}{x} \cdot \left( x+2\right) = x^2+2x $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^2+2x}\right) $ by each term in $ \left( x+4\right) $. $$ \left( \color{blue}{x^2+2x}\right) \cdot \left( x+4\right) = x^3+4x^2+2x^2+8x $$ |
| ③ | Combine like terms: $$ x^3+ \color{blue}{4x^2} + \color{blue}{2x^2} +8x = x^3+ \color{blue}{6x^2} +8x $$ |
| ④ | Multiply each term of $ \left( \color{blue}{x^3+6x^2+8x}\right) $ by each term in $ \left( x+6\right) $. $$ \left( \color{blue}{x^3+6x^2+8x}\right) \cdot \left( x+6\right) = x^4+6x^3+6x^3+36x^2+8x^2+48x $$ |
| ⑤ | Combine like terms: $$ x^4+ \color{blue}{6x^3} + \color{blue}{6x^3} + \color{red}{36x^2} + \color{red}{8x^2} +48x = x^4+ \color{blue}{12x^3} + \color{red}{44x^2} +48x $$ |
This page was created using
Simplify polynomials calculator