Answer
$$(4x^3+2x^2+2x+2.5)(2x-1)-1.5=8x^4+2x^2+2x-3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4x^3+2x^2+2x+2.5)(2x-1)-1.5& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}8x^4+2x^2+2x-2-1.5 \xlongequal{ } \\[1 em] & \xlongequal{ }8x^4+2x^2+2x-2-1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}8x^4+2x^2+2x-3\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{4x^3+2x^2+2x+2}\right) $ by each term in $ \left( 2x-1\right) $. $$ \left( \color{blue}{4x^3+2x^2+2x+2}\right) \cdot \left( 2x-1\right) = \\ = 8x^4 -\cancel{4x^3}+ \cancel{4x^3}-2x^2+4x^2-2x+4x-2 $$ |
| ② | Combine like terms: $$ 8x^4 \, \color{blue}{ -\cancel{4x^3}} \,+ \, \color{blue}{ \cancel{4x^3}} \, \color{green}{-2x^2} + \color{green}{4x^2} \color{orange}{-2x} + \color{orange}{4x} -2 = 8x^4+ \color{green}{2x^2} + \color{orange}{2x} -2 $$ |
| ③ | Combine like terms: $$ 8x^4+2x^2+2x \color{blue}{-2} \color{blue}{-1} = 8x^4+2x^2+2x \color{blue}{-3} $$ |
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