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factor each of the following expressions.
a ( 4 x ^ { 2 } - 64 = )
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b. ( 16 x ^ { 2 } - 1 = )
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Explanation:

Step1: Factor out the greatest common factor (GCF) for \(4x^{2}-64\)

First, find the GCF of \(4x^{2}\) and \(64\). The GCF of \(4\) and \(64\) is \(4\).

$$4x^{2}-64 = 4(x^{2}-16)$$

Then, use the difference - of - squares formula \(a^{2}-b^{2}=(a + b)(a - b)\), where \(a=x\) and \(b = 4\)

$$4(x^{2}-16)=4(x + 4)(x - 4)$$

Step2: Use the difference - of - squares formula for \(16x^{2}-1\)

For the expression \(16x^{2}-1\), we can rewrite it as \((4x)^{2}-1^{2}\)
Using the difference - of - squares formula \(a^{2}-b^{2}=(a + b)(a - b)\), where \(a = 4x\) and \(b=1\)

$$16x^{2}-1=(4x + 1)(4x - 1)$$

Answer:

a. \(4(x + 4)(x - 4)\)
b. \((4x + 1)(4x - 1)\)