Solve (3a+2)^3+(2a+1)^3+a^3=

$$( 3 a + 2 ) ^ { 3 } + ( 2 a + 1 ) ^ { 3 } + a ^ { 3 } =$$

Evaluate

$$36a^{3}+66a^{2}+42a+9$$

Solution Steps

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

$$27a^{3}+54a^{2}+36a+8+\left(2a+1\right)^{3}+a^{3}$$

Use binomial theorem \left(p+q\right)^{3}=p^{3}+3p^{2}q+3pq^{2}+q^{3} to expand \left(2a+1\right)^{3}.

$$27a^{3}+54a^{2}+36a+8+8a^{3}+12a^{2}+6a+1+a^{3}$$

Combine 27a^{3} and 8a^{3} to get 35a^{3}.

$$35a^{3}+54a^{2}+36a+8+12a^{2}+6a+1+a^{3}$$

Combine 54a^{2} and 12a^{2} to get 66a^{2}.

$$35a^{3}+66a^{2}+36a+8+6a+1+a^{3}$$

Combine 36a and 6a to get 42a.

$$35a^{3}+66a^{2}+42a+8+1+a^{3}$$

Add 8 and 1 to get 9.

$$35a^{3}+66a^{2}+42a+9+a^{3}$$

Combine 35a^{3} and a^{3} to get 36a^{3}.

$$36a^{3}+66a^{2}+42a+9$$

Expand

$$36a^{3}+66a^{2}+42a+9$$

Solution Steps

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

$$27a^{3}+54a^{2}+36a+8+\left(2a+1\right)^{3}+a^{3}$$

Use binomial theorem \left(p+q\right)^{3}=p^{3}+3p^{2}q+3pq^{2}+q^{3} to expand \left(2a+1\right)^{3}.

$$27a^{3}+54a^{2}+36a+8+8a^{3}+12a^{2}+6a+1+a^{3}$$

Combine 27a^{3} and 8a^{3} to get 35a^{3}.

$$35a^{3}+54a^{2}+36a+8+12a^{2}+6a+1+a^{3}$$

Combine 54a^{2} and 12a^{2} to get 66a^{2}.

$$35a^{3}+66a^{2}+36a+8+6a+1+a^{3}$$

Combine 36a and 6a to get 42a.

$$35a^{3}+66a^{2}+42a+8+1+a^{3}$$

Add 8 and 1 to get 9.

$$35a^{3}+66a^{2}+42a+9+a^{3}$$

Combine 35a^{3} and a^{3} to get 36a^{3}.

$$36a^{3}+66a^{2}+42a+9$$