Solve a^2(a+1)^2-2(a^2-22a+4)

$$a ^ { 2 } ( a + 1 ) ^ { 2 } - 2 ( a ^ { 2 } - 22 a + 4 )$$

Evaluate

$$\left(a\left(a+1\right)\right)^{2}-2a^{2}+44a-8$$

Solution Steps

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

$$a^{2}\left(a^{2}+2a+1\right)-2\left(a^{2}-22a+4\right)$$

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

$$a^{4}+2a^{3}+a^{2}-2\left(a^{2}-22a+4\right)$$

Use the distributive property to multiply -2 by a^{2}-22a+4.

$$a^{4}+2a^{3}+a^{2}-2a^{2}+44a-8$$

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

$$a^{4}+2a^{3}-a^{2}+44a-8$$

Expand

$$a^{4}+2a^{3}-a^{2}+44a-8$$

Solution Steps

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

$$a^{2}\left(a^{2}+2a+1\right)-2\left(a^{2}-22a+4\right)$$

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

$$a^{4}+2a^{3}+a^{2}-2\left(a^{2}-22a+4\right)$$

Use the distributive property to multiply -2 by a^{2}-22a+4.

$$a^{4}+2a^{3}+a^{2}-2a^{2}+44a-8$$

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

$$a^{4}+2a^{3}-a^{2}+44a-8$$