Solve (4y^3-2)^2

$$( 4 y ^ { 3 } - 2 ) ^ { 2 }$$

Evaluate

$$4\left(2y^{3}-1\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4y^{3}-2\right)^{2}.

$$16\left(y^{3}\right)^{2}-16y^{3}+4$$

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

$$16y^{6}-16y^{3}+4$$

Expand

$$16y^{6}-16y^{3}+4$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4y^{3}-2\right)^{2}.

$$16\left(y^{3}\right)^{2}-16y^{3}+4$$

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

$$16y^{6}-16y^{3}+4$$