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

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

Evaluate

$$\left(9a^{2}-1\right)^{2}$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(3a+1\right)^{2}.

$$\left(9a^{2}+6a+1\right)\left(3a-1\right)^{2}$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(3a-1\right)^{2}.

$$\left(9a^{2}+6a+1\right)\left(9a^{2}-6a+1\right)$$

Use the distributive property to multiply 9a^{2}+6a+1 by 9a^{2}-6a+1 and combine like terms.

$$81a^{4}-18a^{2}+1$$

Expand

$$81a^{4}-18a^{2}+1$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(3a+1\right)^{2}.

$$\left(9a^{2}+6a+1\right)\left(3a-1\right)^{2}$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(3a-1\right)^{2}.

$$\left(9a^{2}+6a+1\right)\left(9a^{2}-6a+1\right)$$

Use the distributive property to multiply 9a^{2}+6a+1 by 9a^{2}-6a+1 and combine like terms.

$$81a^{4}-18a^{2}+1$$