Solve left(t^2+2t+1right)left(t^2-8t+16right)left(2t+3right)

$$\left( { t }^{ 2 } +2t+1 \right) \left( { t }^{ 2 } -8t+16 \right) \left( 2t+3 \right)$$

Evaluate

$$\left(2t+3\right)\left(\left(t-4\right)\left(t+1\right)\right)^{2}$$

Solution Steps

Use the distributive property to multiply t^{2}+2t+1 by t^{2}-8t+16 and combine like terms.

$$\left(t^{4}-6t^{3}+24t+t^{2}+16\right)\left(2t+3\right)$$

Use the distributive property to multiply t^{4}-6t^{3}+24t+t^{2}+16 by 2t+3 and combine like terms.

$$2t^{5}-9t^{4}-16t^{3}+51t^{2}+104t+48$$

Expand

$$2t^{5}-9t^{4}-16t^{3}+51t^{2}+104t+48$$

Solution Steps

Use the distributive property to multiply t^{2}+2t+1 by t^{2}-8t+16 and combine like terms.

$$\left(t^{4}-6t^{3}+24t+t^{2}+16\right)\left(2t+3\right)$$

Use the distributive property to multiply t^{4}-6t^{3}+24t+t^{2}+16 by 2t+3 and combine like terms.

$$2t^{5}-9t^{4}-16t^{3}+51t^{2}+104t+48$$