Solve a^3+8a^2+64a-8a^2-64a-3

$$a ^ { 3 } + 8 a ^ { 2 } + 64 a - 8 a ^ { 2 } - 64 a - 3$$

Evaluate

$$a^{3}-3$$

Solution Steps

Combine 8a^{2} and -8a^{2} to get 0.

$$a^{3}+64a-64a-3$$

Combine 64a and -64a to get 0.

$$a^{3}-3$$

Differentiate w.r.t. a

$$3a^{2}$$

Steps Using Derivative Rule for Sum

Combine 8a^{2} and -8a^{2} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{3}+64a-64a-3)$$

Combine 64a and -64a to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{3}-3)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$3a^{3-1}$$

Subtract 1 from 3.

$$3a^{2}$$