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Chapter 0: Problem 47

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

Short Answer

Expert verified
The product is \(16x^4 - 8x^2 + 1\).

Step by step solution

01

Identify the terms in the binomial

In the expression, the term \(a\) is \(4x^2\) and the term \(b\) is \(1\).
02

Apply the binomial square formula

We substitute \(a\) and \(b\) into the formula: \((4x^2)^2 - 2*(4x^2)*1 + 1^2\).
03

Perform the operations

Calculating the squares and then carrying out the multiplication and addition operations gives us: \(16x^4 - 8x^2 + 1 \).

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Most popular questions from this chapter

Exercises \(142-144\) will help you prepare for the material covered in the next section. Use the distributive property to multiply: $$ 2 x^{4}\left(8 x^{4}+3 x\right) $$

Explain how to find the least common denominator for denominators of \(x^{2}-100\) and \(x^{2}-20 x+100\).

Perform the indicated operations. $$\frac{1}{x^{n}-1}-\frac{1}{x^{n}+1}-\frac{1}{x^{2 n}-1}$$

Explain how to solve \(x^{2}+6 x+8=0\) using the quadratic formula.

What does it mean to solve a formula for a variable?
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