Solve 8a^3-2a(a+1)^2

$$8 a ^ { 3 } - 2 a ( a + 1 ) ^ { 2 }$$

Evaluate

$$2a\left(a-1\right)\left(3a+1\right)$$

Solution Steps

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

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

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

$$8a^{3}-2a^{3}-4a^{2}-2a$$

Combine 8a^{3} and -2a^{3} to get 6a^{3}.

$$6a^{3}-4a^{2}-2a$$

Expand

$$6a^{3}-4a^{2}-2a$$

Solution Steps

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

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

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

$$8a^{3}-2a^{3}-4a^{2}-2a$$

Combine 8a^{3} and -2a^{3} to get 6a^{3}.

$$6a^{3}-4a^{2}-2a$$