Question
Answer
$$(2x+3)(4x^2-6x+9)=8x^3+27$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x+3)(4x^2-6x+9)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}8x^3-12x^2+18x+12x^2-18x+27 \xlongequal{ } \\[1 em] & \xlongequal{ }8x^3 -\cancel{12x^2}+ \cancel{18x}+ \cancel{12x^2} -\cancel{18x}+27 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}8x^3+27\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2x+3}\right) $ by each term in $ \left( 4x^2-6x+9\right) $. $$ \left( \color{blue}{2x+3}\right) \cdot \left( 4x^2-6x+9\right) = \\ = 8x^3 -\cancel{12x^2}+ \cancel{18x}+ \cancel{12x^2} -\cancel{18x}+27 $$ |
| ② | Combine like terms: $$ 8x^3 \, \color{blue}{ -\cancel{12x^2}} \,+ \, \color{green}{ \cancel{18x}} \,+ \, \color{blue}{ \cancel{12x^2}} \, \, \color{green}{ -\cancel{18x}} \,+27 = 8x^3+27 $$ |
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