Solve {l}{(4x^2+1)^2}{-(4x)^2}

$$\left. \begin{array} { l } { ( 4 x ^ { 2 } + 1 ) ^ { 2 } } \\ { - ( 4 x ) ^ { 2 } } \end{array} \right.$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4x^{2}+1\right)^{2}.

$$16\left(x^{2}\right)^{2}+8x^{2}+1-\left(4x\right)^{2}$$

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

$$16x^{4}+8x^{2}+1-\left(4x\right)^{2}$$

Expand \left(4x\right)^{2}.

$$16x^{4}+8x^{2}+1-4^{2}x^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16x^{4}+8x^{2}+1-16x^{2}$$

Combine 8x^{2} and -16x^{2} to get -8x^{2}.

$$16x^{4}-8x^{2}+1$$

Expand

$$16x^{4}-8x^{2}+1$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4x^{2}+1\right)^{2}.

$$16\left(x^{2}\right)^{2}+8x^{2}+1-\left(4x\right)^{2}$$

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

$$16x^{4}+8x^{2}+1-\left(4x\right)^{2}$$

Expand \left(4x\right)^{2}.

$$16x^{4}+8x^{2}+1-4^{2}x^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16x^{4}+8x^{2}+1-16x^{2}$$

Combine 8x^{2} and -16x^{2} to get -8x^{2}.

$$16x^{4}-8x^{2}+1$$