Question

factor each of the following expressions.
a. ( 100 x ^ { 2 } - 4 y ^ { 2 } = )
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b. ( 225 x ^ { 2 } - 16 y ^ { 2 } = )
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Explanation:

Step1: Recall the difference - of - squares formula

The difference - of - squares formula is \(a^{2}-b^{2}=(a + b)(a - b)\).

Step2: Factor \(100x^{2}-4y^{2}\)

Rewrite \(100x^{2}-4y^{2}\) as \((10x)^{2}-(2y)^{2}\).
Using the difference - of - squares formula \(a = 10x\) and \(b=2y\), we get \((10x + 2y)(10x-2y)=4(5x + y)(5x - y)\)

Step3: Factor \(225x^{2}-16y^{2}\)

Rewrite \(225x^{2}-16y^{2}\) as \((15x)^{2}-(4y)^{2}\).
Using the difference - of - squares formula with \(a = 15x\) and \(b = 4y\), we get \((15x+4y)(15x - 4y)\)

Answer:

a. \(4(5x + y)(5x - y)\)
b. \((15x + 4y)(15x - 4y)\)