Solve (a^2-5)^2+8(5-a^2)+16

$$( a ^ { 2 } - 5 ) ^ { 2 } + 8 ( 5 - a ^ { 2 } ) + 16$$

Evaluate

$$\left(a^{2}-9\right)^{2}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a^{2}-5\right)^{2}.

$$\left(a^{2}\right)^{2}-10a^{2}+25+8\left(5-a^{2}\right)+16$$

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

$$a^{4}-10a^{2}+25+8\left(5-a^{2}\right)+16$$

Use the distributive property to multiply 8 by 5-a^{2}.

$$a^{4}-10a^{2}+25+40-8a^{2}+16$$

Add 25 and 40 to get 65.

$$a^{4}-10a^{2}+65-8a^{2}+16$$

Combine -10a^{2} and -8a^{2} to get -18a^{2}.

$$a^{4}-18a^{2}+65+16$$

Add 65 and 16 to get 81.

$$a^{4}-18a^{2}+81$$

Expand

$$a^{4}-18a^{2}+81$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a^{2}-5\right)^{2}.

$$\left(a^{2}\right)^{2}-10a^{2}+25+8\left(5-a^{2}\right)+16$$

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

$$a^{4}-10a^{2}+25+8\left(5-a^{2}\right)+16$$

Use the distributive property to multiply 8 by 5-a^{2}.

$$a^{4}-10a^{2}+25+40-8a^{2}+16$$

Add 25 and 40 to get 65.

$$a^{4}-10a^{2}+65-8a^{2}+16$$

Combine -10a^{2} and -8a^{2} to get -18a^{2}.

$$a^{4}-18a^{2}+65+16$$

Add 65 and 16 to get 81.

$$a^{4}-18a^{2}+81$$