Question
Answer
$$v(h+3v)\cdot(1+h^2)+h(v+3h)\cdot(1+v^2)-4\cdot(1+v^2)\cdot(1+h^2)=h^3v+2h^2v^2+hv^3-h^2+2hv-v^2-4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}v(h+3v)\cdot(1+h^2)+h(v+3h)\cdot(1+v^2)-4\cdot(1+v^2)\cdot(1+h^2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1hv+3v^2)\cdot(1+h^2)+(1hv+3h^2)\cdot(1+v^2)-(4+4v^2)\cdot(1+h^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}hv+h^3v+3v^2+3h^2v^2+hv+hv^3+3h^2+3h^2v^2-(4+4h^2+4v^2+4h^2v^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}h^3v+6h^2v^2+hv^3+3h^2+2hv+3v^2-(4+4h^2+4v^2+4h^2v^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}h^3v+6h^2v^2+hv^3+3h^2+2hv+3v^2-4-4h^2-4v^2-4h^2v^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}h^3v+2h^2v^2+hv^3-h^2+2hv-v^2-4\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{v} $ by $ \left( h+3v\right) $ $$ \color{blue}{v} \cdot \left( h+3v\right) = hv+3v^2 $$Multiply $ \color{blue}{h} $ by $ \left( v+3h\right) $ $$ \color{blue}{h} \cdot \left( v+3h\right) = hv+3h^2 $$Multiply $ \color{blue}{4} $ by $ \left( 1+v^2\right) $ $$ \color{blue}{4} \cdot \left( 1+v^2\right) = 4+4v^2 $$ |
| ② | Multiply each term of $ \left( \color{blue}{hv+3v^2}\right) $ by each term in $ \left( 1+h^2\right) $. $$ \left( \color{blue}{hv+3v^2}\right) \cdot \left( 1+h^2\right) = hv+h^3v+3v^2+3h^2v^2 $$Multiply each term of $ \left( \color{blue}{hv+3h^2}\right) $ by each term in $ \left( 1+v^2\right) $. $$ \left( \color{blue}{hv+3h^2}\right) \cdot \left( 1+v^2\right) = hv+hv^3+3h^2+3h^2v^2 $$Multiply each term of $ \left( \color{blue}{4+4v^2}\right) $ by each term in $ \left( 1+h^2\right) $. $$ \left( \color{blue}{4+4v^2}\right) \cdot \left( 1+h^2\right) = 4+4h^2+4v^2+4h^2v^2 $$ |
| ③ | Combine like terms: $$ \color{blue}{hv} +h^3v+3v^2+ \color{red}{3h^2v^2} + \color{blue}{hv} +hv^3+3h^2+ \color{red}{3h^2v^2} = h^3v+ \color{red}{6h^2v^2} +hv^3+3h^2+ \color{blue}{2hv} +3v^2 $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 4+4h^2+4v^2+4h^2v^2 \right) = -4-4h^2-4v^2-4h^2v^2 $$ |
| ⑤ | Combine like terms: $$ h^3v+ \color{blue}{6h^2v^2} +hv^3+ \color{red}{3h^2} +2hv+ \color{green}{3v^2} -4 \color{red}{-4h^2} \color{green}{-4v^2} \color{blue}{-4h^2v^2} = \\ = h^3v+ \color{blue}{2h^2v^2} +hv^3 \color{red}{-h^2} +2hv \color{green}{-v^2} -4 $$ |
This page was created using
Simplify polynomials calculator