Solve a-a^2-1)^2-3(a+2)^2=a^3(a-1)+a[(a+2)(1-a)+a]

$$a - a ^ { 2 } - 1 ) ^ { 2 } - 3 ( a + 2 ) ^ { 2 } = a ^ { 3 } ( a - 1 ) + a [ ( a + 2 ) ( 1 - a ) + a ]$$

Differentiate w.r.t. a

$$1-2a$$

Steps Using Derivative Rule for Sum

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}.

$$a^{1-1}+2\left(-1\right)a^{2-1}$$

Subtract 1 from 1.

$$a^{0}+2\left(-1\right)a^{2-1}$$

Multiply 2 times -1.

$$a^{0}-2a^{2-1}$$

Subtract 1 from 2.

$$a^{0}-2a^{1}$$

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

$$a^{0}-2a$$

For any term t except 0, t^{0}=1.

$$1-2a$$

Evaluate

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