Solve 343-(a+4)^3

$$343 - ( a + 4 ) ^ { 3 }$$

Evaluate

$$\left(3-a\right)\left(a^{2}+15a+93\right)$$

Solution Steps

Use binomial theorem \left(p+q\right)^{3}=p^{3}+3p^{2}q+3pq^{2}+q^{3} to expand \left(a+4\right)^{3}.

$$343-\left(a^{3}+12a^{2}+48a+64\right)$$

To find the opposite of a^{3}+12a^{2}+48a+64, find the opposite of each term.

$$343-a^{3}-12a^{2}-48a-64$$

Subtract 64 from 343 to get 279.

$$279-a^{3}-12a^{2}-48a$$

Expand

$$279-48a-12a^{2}-a^{3}$$

Solution Steps

Use binomial theorem \left(p+q\right)^{3}=p^{3}+3p^{2}q+3pq^{2}+q^{3} to expand \left(a+4\right)^{3}.

$$343-\left(a^{3}+12a^{2}+48a+64\right)$$

To find the opposite of a^{3}+12a^{2}+48a+64, find the opposite of each term.

$$343-a^{3}-12a^{2}-48a-64$$

Subtract 64 from 343 to get 279.

$$279-a^{3}-12a^{2}-48a$$