Solve 5(a+3)^3-2(a+3)+(a+3)^2

$$5 ( a + 3 ) ^ { 3 } - 2 ( a + 3 ) + ( a + 3 ) ^ { 2 }$$

Evaluate

$$\left(a+3\right)\left(5\left(a+3\right)^{2}+a+1\right)$$

Solution Steps

Use binomial theorem \left(p+q\right)^{3}=p^{3}+3p^{2}q+3pq^{2}+q^{3} to expand \left(a+3\right)^{3}.

$$5\left(a^{3}+9a^{2}+27a+27\right)-2\left(a+3\right)+\left(a+3\right)^{2}$$

Use the distributive property to multiply 5 by a^{3}+9a^{2}+27a+27.

$$5a^{3}+45a^{2}+135a+135-2\left(a+3\right)+\left(a+3\right)^{2}$$

Use the distributive property to multiply -2 by a+3.

$$5a^{3}+45a^{2}+135a+135-2a-6+\left(a+3\right)^{2}$$

Combine 135a and -2a to get 133a.

$$5a^{3}+45a^{2}+133a+135-6+\left(a+3\right)^{2}$$

Subtract 6 from 135 to get 129.

$$5a^{3}+45a^{2}+133a+129+\left(a+3\right)^{2}$$

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+3\right)^{2}.

$$5a^{3}+45a^{2}+133a+129+a^{2}+6a+9$$

Combine 45a^{2} and a^{2} to get 46a^{2}.

$$5a^{3}+46a^{2}+133a+129+6a+9$$

Combine 133a and 6a to get 139a.

$$5a^{3}+46a^{2}+139a+129+9$$

Add 129 and 9 to get 138.

$$5a^{3}+46a^{2}+139a+138$$

Expand

$$5a^{3}+46a^{2}+139a+138$$

Solution Steps

Use binomial theorem \left(p+q\right)^{3}=p^{3}+3p^{2}q+3pq^{2}+q^{3} to expand \left(a+3\right)^{3}.

$$5\left(a^{3}+9a^{2}+27a+27\right)-2\left(a+3\right)+\left(a+3\right)^{2}$$

Use the distributive property to multiply 5 by a^{3}+9a^{2}+27a+27.

$$5a^{3}+45a^{2}+135a+135-2\left(a+3\right)+\left(a+3\right)^{2}$$

Use the distributive property to multiply -2 by a+3.

$$5a^{3}+45a^{2}+135a+135-2a-6+\left(a+3\right)^{2}$$

Combine 135a and -2a to get 133a.

$$5a^{3}+45a^{2}+133a+135-6+\left(a+3\right)^{2}$$

Subtract 6 from 135 to get 129.

$$5a^{3}+45a^{2}+133a+129+\left(a+3\right)^{2}$$

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+3\right)^{2}.

$$5a^{3}+45a^{2}+133a+129+a^{2}+6a+9$$

Combine 45a^{2} and a^{2} to get 46a^{2}.

$$5a^{3}+46a^{2}+133a+129+6a+9$$

Combine 133a and 6a to get 139a.

$$5a^{3}+46a^{2}+139a+129+9$$

Add 129 and 9 to get 138.

$$5a^{3}+46a^{2}+139a+138$$