# How do you find the product (m^2-5m+4)(m^2+7m-3)?

Aug 21, 2017

See a solution process below:

#### Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{{m}^{2}} - \textcolor{red}{5 m} + \textcolor{red}{4}\right) \left(\textcolor{b l u e}{{m}^{2}} + \textcolor{b l u e}{7 m} - \textcolor{b l u e}{3}\right)$ becomes:

$\left(\textcolor{red}{{m}^{2}} \times \textcolor{b l u e}{{m}^{2}}\right) + \left(\textcolor{red}{{m}^{2}} \times \textcolor{b l u e}{7 m}\right) - \left(\textcolor{red}{{m}^{2}} \times \textcolor{b l u e}{3}\right) - \left(\textcolor{red}{5 m} \times \textcolor{b l u e}{{m}^{2}}\right) - \left(\textcolor{red}{5 m} \times \textcolor{b l u e}{7 m}\right) + \left(\textcolor{red}{5 m} \times \textcolor{b l u e}{3}\right) + \left(\textcolor{red}{4} \times \textcolor{b l u e}{{m}^{2}}\right) + \left(\textcolor{red}{4} \times \textcolor{b l u e}{7 m}\right) - \left(\textcolor{red}{4} \times \textcolor{b l u e}{3}\right)$

${m}^{4} + 7 {m}^{3} - 3 {m}^{2} - 5 {m}^{3} - 35 {m}^{2} + 15 m + 4 {m}^{2} + 28 m - 12$

We can now group and combine like terms:

${m}^{4} + 7 {m}^{3} - 5 {m}^{3} - 3 {m}^{2} - 35 {m}^{2} + 4 {m}^{2} + 15 m + 28 m - 12$

${m}^{4} + \left(7 - 5\right) {m}^{3} + \left(- 3 - 35 + 4\right) {m}^{2} + \left(15 + 28\right) m - 12$

${m}^{4} + 2 {m}^{3} + \left(- 34\right) {m}^{2} + 43 m - 12$

${m}^{4} + 2 {m}^{3} - 34 {m}^{2} + 43 m - 12$