Question

factor each of the following expressions
a ( 16 x ^ { 4 } - 36 = )

b ( 144 x ^ { 4 } - 49 y ^ { 4 } = )
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Explanation:

Step1: Factor out the greatest common factor (GCF)

For \(16x^{4}-36\), the GCF of \(16\) and \(36\) is \(4\). So, \(16x^{4}-36 = 4(4x^{4}-9)\).
For \(144x^{4}-49y^{4}\), there is no GCF other than \(1\).

Step2: Use the difference - of - squares formula \(a^{2}-b^{2}=(a + b)(a - b)\)

For \(4x^{4}-9=(2x^{2})^{2}-3^{2}\), by the difference - of - squares formula, \(4x^{4}-9=(2x^{2}+3)(2x^{2}-3)\). So, \(16x^{4}-36=4(2x^{2}+3)(2x^{2}-3)\).
For \(144x^{4}-49y^{4}=(12x^{2})^{2}-(7y^{2})^{2}\), using the difference - of - squares formula, \(144x^{4}-49y^{4}=(12x^{2}+7y^{2})(12x^{2}-7y^{2})\)

Answer:

a. \(4(2x^{2}+3)(2x^{2}-3)\)
b. \((12x^{2}+7y^{2})(12x^{2}-7y^{2})\)