Find the product using the distributive property classify/name your final answer (x+5) (3x^2-2x+1)

Distribute sum groups

x (3{x}^{2}-2x+1) + 5 (3{x}^{2}-2x+1) x (3 x 2 - 2x+1) + 5 (3 x 2 - 2x+1)

2 Distribute

3{x}^{3}-2{x}^{2}+x+5 (3{x}^{2}-2x+1) 3 x 3 - 2 x 2 + x+5 (3 x 2 - 2x+1)

3 Distribute

3{x}^{3}-2{x}^{2}+x+15{x}^{2}-10x+5 3 x 3 - 2 x 2 + x+15 x 2 - 10x+5

4 Collect like terms

3{x}^{3} + (-2{x}^{2}+15{x}^{2}) + (x-10x) + 5 3 x 3 + (-2 x 2 + 15 x 2 ) + (x-10x) + 5

5 Simplify

3{x}^{3}+13{x}^{2}-9x+5 3 x 3 + 13 x 2 - 9x + 5