Tap the blue circles to see an explanation.
$$ \begin{aligned}(x^2+7)(4x-3)\cdot(5-2x)(x-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(4x^3-3x^2+28x-21)\cdot(5-2x)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(-8x^4+26x^3-71x^2+182x-105)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-8x^5+34x^4-97x^3+253x^2-287x+105\end{aligned} $$ | |
① | Multiply each term of $ \left( \color{blue}{x^2+7}\right) $ by each term in $ \left( 4x-3\right) $. $$ \left( \color{blue}{x^2+7}\right) \cdot \left( 4x-3\right) = 4x^3-3x^2+28x-21 $$ |
② | Multiply each term of $ \left( \color{blue}{4x^3-3x^2+28x-21}\right) $ by each term in $ \left( 5-2x\right) $. $$ \left( \color{blue}{4x^3-3x^2+28x-21}\right) \cdot \left( 5-2x\right) = 20x^3-8x^4-15x^2+6x^3+140x-56x^2-105+42x $$ |
③ | Combine like terms: $$ \color{blue}{20x^3} -8x^4 \color{red}{-15x^2} + \color{blue}{6x^3} + \color{green}{140x} \color{red}{-56x^2} -105+ \color{green}{42x} = \\ = -8x^4+ \color{blue}{26x^3} \color{red}{-71x^2} + \color{green}{182x} -105 $$ |
④ | Multiply each term of $ \left( \color{blue}{-8x^4+26x^3-71x^2+182x-105}\right) $ by each term in $ \left( x-1\right) $. $$ \left( \color{blue}{-8x^4+26x^3-71x^2+182x-105}\right) \cdot \left( x-1\right) = \\ = -8x^5+8x^4+26x^4-26x^3-71x^3+71x^2+182x^2-182x-105x+105 $$ |
⑤ | Combine like terms: $$ -8x^5+ \color{blue}{8x^4} + \color{blue}{26x^4} \color{red}{-26x^3} \color{red}{-71x^3} + \color{green}{71x^2} + \color{green}{182x^2} \color{orange}{-182x} \color{orange}{-105x} +105 = \\ = -8x^5+ \color{blue}{34x^4} \color{red}{-97x^3} + \color{green}{253x^2} \color{orange}{-287x} +105 $$ |