Solve 9w^2(w^2+2w+1)-8(w^2+2w+1)

$$9 w ^ { 2 } ( w ^ { 2 } + 2 w + 1 ) - 8 ( w ^ { 2 } + 2 w + 1 )$$

Evaluate

$$\left(9w^{2}-8\right)\left(w+1\right)^{2}$$

Solution Steps

Use the distributive property to multiply 9w^{2} by w^{2}+2w+1.

$$9w^{4}+18w^{3}+9w^{2}-8\left(w^{2}+2w+1\right)$$

Use the distributive property to multiply -8 by w^{2}+2w+1.

$$9w^{4}+18w^{3}+9w^{2}-8w^{2}-16w-8$$

Combine 9w^{2} and -8w^{2} to get w^{2}.

$$9w^{4}+18w^{3}+w^{2}-16w-8$$

Expand

$$9w^{4}+18w^{3}+w^{2}-16w-8$$

Solution Steps

Use the distributive property to multiply 9w^{2} by w^{2}+2w+1.

$$9w^{4}+18w^{3}+9w^{2}-8\left(w^{2}+2w+1\right)$$

Use the distributive property to multiply -8 by w^{2}+2w+1.

$$9w^{4}+18w^{3}+9w^{2}-8w^{2}-16w-8$$

Combine 9w^{2} and -8w^{2} to get w^{2}.

$$9w^{4}+18w^{3}+w^{2}-16w-8$$