Solve (a^2-a)^2-a^2-6a-a

$$( a ^ { 2 } - a ) ^ { 2 } - a ^ { 2 } - 6 a - a$$

Evaluate

$$a\left(a^{3}-2a^{2}-7\right)$$

Solution Steps

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

$$\left(a^{2}\right)^{2}-2a^{2}a+a^{2}-a^{2}-6a-a$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$a^{4}-2a^{2}a+a^{2}-a^{2}-6a-a$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$a^{4}-2a^{3}+a^{2}-a^{2}-6a-a$$

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

$$a^{4}-2a^{3}-6a-a$$

Combine -6a and -a to get -7a.

$$a^{4}-2a^{3}-7a$$

Expand

$$a^{4}-2a^{3}-7a$$

Solution Steps

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

$$\left(a^{2}\right)^{2}-2a^{2}a+a^{2}-a^{2}-6a-a$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$a^{4}-2a^{2}a+a^{2}-a^{2}-6a-a$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$a^{4}-2a^{3}+a^{2}-a^{2}-6a-a$$

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

$$a^{4}-2a^{3}-6a-a$$

Combine -6a and -a to get -7a.

$$a^{4}-2a^{3}-7a$$