How do you find the product of (m+3)(m^2+3m+5)?

Aug 14, 2016

${m}^{3} + 6 {m}^{2} + 14 m + 15$

Explanation:

$\left(m + 3\right) \left({m}^{2} + 3 m + 5\right)$

To expand the polynomial multiply each element of the first term by each element of the second term and then combine the coefficients of each power.

$\left(m + 3\right) \left({m}^{2} + 3 m + 5\right) = m \left({m}^{2} + 3 m + 5\right) + 3 \left({m}^{2} + 3 m + 5\right)$

$= {m}^{3} + 3 {m}^{2} + 5 m + 3 {m}^{2} + 9 m + 15$

$= {m}^{3} + \left(3 + 3\right) {m}^{2} + \left(5 + 9\right) m + 15$

$= {m}^{3} + 6 {m}^{2} + 14 m + 15$