Solve (3a-2a^3)^2

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

Evaluate

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

Solution Steps

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

$$9a^{2}-12aa^{3}+4\left(a^{3}\right)^{2}$$

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

$$9a^{2}-12a^{4}+4\left(a^{3}\right)^{2}$$

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

$$9a^{2}-12a^{4}+4a^{6}$$

Expand

$$4a^{6}-12a^{4}+9a^{2}$$

Solution Steps

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

$$9a^{2}-12aa^{3}+4\left(a^{3}\right)^{2}$$

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

$$9a^{2}-12a^{4}+4\left(a^{3}\right)^{2}$$

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

$$9a^{2}-12a^{4}+4a^{6}$$