Tap the blue circles to see an explanation.
$$ \begin{aligned}(0.3-2x)^2(0.6-3x)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(0+0x+4x^2)(0+0x+0x^2-27x^3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-108x^5\end{aligned} $$ | |
① | Find $ \left(0-2x\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 0 } $ and $ B = \color{red}{ 2x }$. $$ \begin{aligned}\left(0-2x\right)^2 = \color{blue}{0^2} -2 \cdot 0 \cdot 2x + \color{red}{\left( 2x \right)^2} = 00x+4x^2\end{aligned} $$Find $ \left(0-3x\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = 0 $ and $ B = 3x $. $$ \left(0-3x\right)^3 = 0^3-3 \cdot 0^2 \cdot 3x + 3 \cdot 0 \cdot \left( 3x \right)^2-\left( 3x \right)^3 = 00x0x^2-27x^3 $$ |
② | Multiply each term of $ \left( \color{blue}{00x+4x^2}\right) $ by each term in $ \left( 00x0x^2-27x^3\right) $. $$ \left( \color{blue}{00x+4x^2}\right) \cdot \left( 00x0x^2-27x^3\right) = \\ = 0 \cancel{0x} \cancel{0x^2} \cancel{0x^3} \cancel{0x} \cancel{0x^2} \cancel{0x^3} \cancel{0x^4} \cancel{0x^2} \cancel{0x^3} \cancel{0x^4}-108x^5 $$ |
③ | Combine like terms: $$ 0 \, \color{blue}{ \cancel{0x}} \, \, \color{green}{ \cancel{0x^2}} \, \, \color{blue}{ \cancel{0x^3}} \, \, \color{blue}{ \cancel{0x}} \, \, \color{green}{ \cancel{0x^2}} \, \, \color{blue}{ \cancel{0x^3}} \, \, \color{green}{ \cancel{0x^4}} \, \, \color{green}{ \cancel{0x^2}} \, \, \color{blue}{ \cancel{0x^3}} \, \, \color{green}{ \cancel{0x^4}} \,-108x^5 = -108x^5 $$ |