Solve (a^2-5a)^2-36

$$( a ^ { 2 } - 5 a ) ^ { 2 } - 36$$

Evaluate

$$\left(a-6\right)\left(a-3\right)\left(a-2\right)\left(a+1\right)$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a^{2}-5a\right)^{2}.

$$\left(a^{2}\right)^{2}-10a^{2}a+25a^{2}-36$$

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

$$a^{4}-10a^{2}a+25a^{2}-36$$

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

$$a^{4}-10a^{3}+25a^{2}-36$$

Expand

$$a^{4}-10a^{3}+25a^{2}-36$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a^{2}-5a\right)^{2}.

$$\left(a^{2}\right)^{2}-10a^{2}a+25a^{2}-36$$

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

$$a^{4}-10a^{2}a+25a^{2}-36$$

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

$$a^{4}-10a^{3}+25a^{2}-36$$