Solve (a^3-6a)^2

$$( a ^ { 3 } - 6 a ) ^ { 2 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a^{3}-6a\right)^{2}.

$$\left(a^{3}\right)^{2}-12a^{3}a+36a^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$a^{6}-12a^{3}a+36a^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$a^{6}-12a^{4}+36a^{2}$$

Expand

$$a^{6}-12a^{4}+36a^{2}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a^{3}-6a\right)^{2}.

$$\left(a^{3}\right)^{2}-12a^{3}a+36a^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$a^{6}-12a^{3}a+36a^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$a^{6}-12a^{4}+36a^{2}$$