Solve a^2+a+1(a^2-a-1)

$$a ^ { 2 } + a + 1 ( a ^ { 2 } - a - 1 )$$

Evaluate

$$2a^{2}-1$$

Solution Steps

Use the distributive property to multiply 1 by a^{2}-a-1.

$$a^{2}+a+a^{2}-a-1$$

Combine a^{2} and a^{2} to get 2a^{2}.

$$2a^{2}+a-a-1$$

Combine a and -a to get 0.

$$2a^{2}-1$$

Differentiate w.r.t. a

$$4a$$

Steps Using Derivative Rule for Sum

Use the distributive property to multiply 1 by a^{2}-a-1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{2}+a+a^{2}-a-1)$$

Combine a^{2} and a^{2} to get 2a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a^{2}+a-a-1)$$

Combine a and -a to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a^{2}-1)$$

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}.

$$2\times 2a^{2-1}$$

Multiply 2 times 2.

$$4a^{2-1}$$

Subtract 1 from 2.

$$4a^{1}$$

For any term t, t^{1}=t.

$$4a$$