Solve (4x^2+7)^2

$$( 4 x ^ { 2 } + 7 ) ^ { 2 }$$

Expand

$$16x^{4}+56x^{2}+49$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4x^{2}+7\right)^{2}.

$$16\left(x^{2}\right)^{2}+56x^{2}+49$$

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

$$16x^{4}+56x^{2}+49$$

Evaluate

$$\left(4x^{2}+7\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4x^{2}+7\right)^{2}.

$$16\left(x^{2}\right)^{2}+56x^{2}+49$$

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

$$16x^{4}+56x^{2}+49$$