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.

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 \(7x^2\)