Solve (t^2+6t+3)(10t)+(2t+6)(5t^2+5)

$$( t ^ { 2 } + 6 t + 3 ) ( 10 t ) + ( 2 t + 6 ) ( 5 t ^ { 2 } + 5 )$$

Evaluate

$$20t^{3}+90t^{2}+40t+30$$

Solution Steps

Use the distributive property to multiply t^{2}+6t+3 by 10.

$$\left(10t^{2}+60t+30\right)t+\left(2t+6\right)\left(5t^{2}+5\right)$$

Use the distributive property to multiply 10t^{2}+60t+30 by t.

$$10t^{3}+60t^{2}+30t+\left(2t+6\right)\left(5t^{2}+5\right)$$

Use the distributive property to multiply 2t+6 by 5t^{2}+5.

$$10t^{3}+60t^{2}+30t+10t^{3}+10t+30t^{2}+30$$

Combine 10t^{3} and 10t^{3} to get 20t^{3}.

$$20t^{3}+60t^{2}+30t+10t+30t^{2}+30$$

Combine 30t and 10t to get 40t.

$$20t^{3}+60t^{2}+40t+30t^{2}+30$$

Combine 60t^{2} and 30t^{2} to get 90t^{2}.

$$20t^{3}+90t^{2}+40t+30$$

Expand

$$20t^{3}+90t^{2}+40t+30$$

Solution Steps

Use the distributive property to multiply t^{2}+6t+3 by 10.

$$\left(10t^{2}+60t+30\right)t+\left(2t+6\right)\left(5t^{2}+5\right)$$

Use the distributive property to multiply 10t^{2}+60t+30 by t.

$$10t^{3}+60t^{2}+30t+\left(2t+6\right)\left(5t^{2}+5\right)$$

Use the distributive property to multiply 2t+6 by 5t^{2}+5.

$$10t^{3}+60t^{2}+30t+10t^{3}+10t+30t^{2}+30$$

Combine 10t^{3} and 10t^{3} to get 20t^{3}.

$$20t^{3}+60t^{2}+30t+10t+30t^{2}+30$$

Combine 30t and 10t to get 40t.

$$20t^{3}+60t^{2}+40t+30t^{2}+30$$

Combine 60t^{2} and 30t^{2} to get 90t^{2}.

$$20t^{3}+90t^{2}+40t+30$$