Problem 47 - College Algebra

Question

Find each product. $$\left(4 x^{2}-1\right)^{2}$$

Step-by-Step Solution

Answer

The result of the squared binomial \((4 x^{2}-1)^{2}\) is \(16x^{4} - 8x^{2} + 1\).

Step 1: Identify the terms

Firstly, identify the terms in the binomial. The binomial \((4 x^{2}-1)\) has \(a = 4x^{2}\) and \(b = -1\).

Step 2: Apply the square of a binomial formula

Now, apply the square of a binomial formula \((a+b)^{2} = a^{2} + 2ab + b^{2}\). In this case, \((4x^{2} - 1)^{2} = (4x^{2})^2 + 2(4x^{2})(-1) + (-1)^2\).

Step 3: Solve for the product

Calculating each term, we get \(16x^{4} - 8x^{2} + 1\).