Answer
$$3(x^2+3x-7)^2(2x+3)=6x^5+45x^4+24x^3-297x^2-84x+441$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3(x^2+3x-7)^2(2x+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3(x^4+6x^3-5x^2-42x+49)(2x+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(3x^4+18x^3-15x^2-126x+147)(2x+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}6x^5+45x^4+24x^3-297x^2-84x+441\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2+3x-7}\right) $ by each term in $ \left( x^2+3x-7\right) $. $$ \left( \color{blue}{x^2+3x-7}\right) \cdot \left( x^2+3x-7\right) = x^4+3x^3-7x^2+3x^3+9x^2-21x-7x^2-21x+49 $$ |
| ② | Combine like terms: $$ x^4+ \color{blue}{3x^3} \color{red}{-7x^2} + \color{blue}{3x^3} + \color{green}{9x^2} \color{orange}{-21x} \color{green}{-7x^2} \color{orange}{-21x} +49 = \\ = x^4+ \color{blue}{6x^3} \color{green}{-5x^2} \color{orange}{-42x} +49 $$ |
| ③ | Multiply $ \color{blue}{3} $ by $ \left( x^4+6x^3-5x^2-42x+49\right) $ $$ \color{blue}{3} \cdot \left( x^4+6x^3-5x^2-42x+49\right) = 3x^4+18x^3-15x^2-126x+147 $$ |
| ④ | Multiply each term of $ \left( \color{blue}{3x^4+18x^3-15x^2-126x+147}\right) $ by each term in $ \left( 2x+3\right) $. $$ \left( \color{blue}{3x^4+18x^3-15x^2-126x+147}\right) \cdot \left( 2x+3\right) = \\ = 6x^5+9x^4+36x^4+54x^3-30x^3-45x^2-252x^2-378x+294x+441 $$ |
| ⑤ | Combine like terms: $$ 6x^5+ \color{blue}{9x^4} + \color{blue}{36x^4} + \color{red}{54x^3} \color{red}{-30x^3} \color{green}{-45x^2} \color{green}{-252x^2} \color{orange}{-378x} + \color{orange}{294x} +441 = \\ = 6x^5+ \color{blue}{45x^4} + \color{red}{24x^3} \color{green}{-297x^2} \color{orange}{-84x} +441 $$ |
This page was created using
Simplify polynomials calculator