Solve partial^6-(a+2)^3

$$\partial ^ { 6 } - ( a + 2 ) ^ { 3 }$$

Evaluate

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

Solution Steps

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

$$∂^{6}-\left(a^{3}+6a^{2}+12a+8\right)$$

To find the opposite of a^{3}+6a^{2}+12a+8, find the opposite of each term.

$$∂^{6}-a^{3}-6a^{2}-12a-8$$

Expand

$$∂^{6}-a^{3}-6a^{2}-12a-8$$

Solution Steps

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

$$∂^{6}-\left(a^{3}+6a^{2}+12a+8\right)$$

To find the opposite of a^{3}+6a^{2}+12a+8, find the opposite of each term.

$$∂^{6}-a^{3}-6a^{2}-12a-8$$