Given two algebraic expressions (4x^2 cos^2 y + 9x^2 sin^2 y) and (5x^2 cos^2 y + 2x^2 sin^2 y), find the greatest common factor (GCF) and simplify the expressions.

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Step:1 ：First, recognize that both expressions have (x^2) in common, so we can factor that out: (x^2 (4 cos^2 y + 9 sin^2 y)) and (x^2 (5 cos^2 y + 2 sin^2 y))Step:2 ：Next, notice that the trigonometric parts in both expressions also have (cos^2 y) and (sin^2 y) in common. So, we can write them as a single term, using the identity (cos^2 y + sin^2 y = 1): (x^2 (4 + 9)) and (x^2 (5 + 2))Step:3 ：Now, simplify each expression to find: (13x^2) and (7x^2)

Answer

Step: 1 ：First, recognize that both expressions have (x^2) in common, so we can factor that out: (x^2 (4 cos^2 y + 9 sin^2 y)) and (x^2 (5 cos^2 y + 2 sin^2 y))Step: 2 ：Next, notice that the trigonometric parts in both expressions also have (cos^2 y) and (sin^2 y) in common. So, we can write them as a single term, using the identity (cos^2 y + sin^2 y = 1): (x^2 (4 + 9)) and (x^2 (5 + 2))Step: 3 ：Now, simplify each expression to find: (13x^2) and (7x^2)

Given two algebraic expressions \(4x^2 \cos^2 y + 9x^2 \sin^2 y\) and \(5x^2 \cos^2 y + 2x^2 \sin^2 y\), find the greatest common factor (GCF) and simplify the expressions.

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