Solve (6+8k^2)^2

$$( 6 + 8 k ^ { 2 } ) ^ { 2 }$$

Evaluate

$$4\left(4k^{2}+3\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(6+8k^{2}\right)^{2}.

$$36+96k^{2}+64\left(k^{2}\right)^{2}$$

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

$$36+96k^{2}+64k^{4}$$

Expand

$$64k^{4}+96k^{2}+36$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(6+8k^{2}\right)^{2}.

$$36+96k^{2}+64\left(k^{2}\right)^{2}$$

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

$$36+96k^{2}+64k^{4}$$