Solve (d+4)^3-2d^3-6d^2

$$( d + 4 ) ^ { 3 } - 2 d ^ { 3 } - 6 d ^ { 2 }$$

Evaluate

$$\left(d+2\right)\left(32+8d-d^{2}\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(d+4\right)^{3}.

$$d^{3}+12d^{2}+48d+64-2d^{3}-6d^{2}$$

Combine d^{3} and -2d^{3} to get -d^{3}.

$$-d^{3}+12d^{2}+48d+64-6d^{2}$$

Combine 12d^{2} and -6d^{2} to get 6d^{2}.

$$-d^{3}+6d^{2}+48d+64$$

Expand

$$64+48d+6d^{2}-d^{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(d+4\right)^{3}.

$$d^{3}+12d^{2}+48d+64-2d^{3}-6d^{2}$$

Combine d^{3} and -2d^{3} to get -d^{3}.

$$-d^{3}+12d^{2}+48d+64-6d^{2}$$

Combine 12d^{2} and -6d^{2} to get 6d^{2}.

$$-d^{3}+6d^{2}+48d+64$$