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

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

Evaluate

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

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

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

Combine 4a^{2} and -2a^{2} to get 2a^{2}.

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

Expand

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

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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

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

Combine 4a^{2} and -2a^{2} to get 2a^{2}.

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