Solve (a+1)(a-1)(a+3)(a-3)

$$( a + 1 ) ( a - 1 ) ( a + 3 ) ( a - 3 )$$

Evaluate

$$a^{4}-10a^{2}+9$$

Solution Steps

Apply the distributive property by multiplying each term of a+1 by each term of a-1.

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

Combine -a and a to get 0.

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

Apply the distributive property by multiplying each term of a^{2}-1 by each term of a+3.

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

Apply the distributive property by multiplying each term of a^{3}+3a^{2}-a-3 by each term of a-3.

$$a^{4}-3a^{3}+3a^{3}-9a^{2}-a^{2}+3a-3a+9$$

Combine -3a^{3} and 3a^{3} to get 0.

$$a^{4}-9a^{2}-a^{2}+3a-3a+9$$

Combine -9a^{2} and -a^{2} to get -10a^{2}.

$$a^{4}-10a^{2}+3a-3a+9$$

Combine 3a and -3a to get 0.

$$a^{4}-10a^{2}+9$$

Expand

$$a^{4}-10a^{2}+9$$

Solution Steps

Apply the distributive property by multiplying each term of a+1 by each term of a-1.

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

Combine -a and a to get 0.

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

Apply the distributive property by multiplying each term of a^{2}-1 by each term of a+3.

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

Apply the distributive property by multiplying each term of a^{3}+3a^{2}-a-3 by each term of a-3.

$$a^{4}-3a^{3}+3a^{3}-9a^{2}-a^{2}+3a-3a+9$$

Combine -3a^{3} and 3a^{3} to get 0.

$$a^{4}-9a^{2}-a^{2}+3a-3a+9$$

Combine -9a^{2} and -a^{2} to get -10a^{2}.

$$a^{4}-10a^{2}+3a-3a+9$$

Combine 3a and -3a to get 0.

$$a^{4}-10a^{2}+9$$