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Chapter 0: Problem 47

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

Short Answer

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

Step by step solution

01

Identify the terms

Firstly, identify the terms in the binomial. The binomial \((4 x^{2}-1)\) has \(a = 4x^{2}\) and \(b = -1\).
02

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, \((4x^{2} - 1)^{2} = (4x^{2})^2 + 2(4x^{2})(-1) + (-1)^2\).
03

Solve for the product

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

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