Solve (a+3)^2(a^2-6a+9)=

$$( a + 3 ) ^ { 2 } ( a ^ { 2 } - 6 a + 9 ) =$$

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+3\right)^{2}.

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

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

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

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+3\right)^{2}.

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

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

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