Simplify the expression (3x + 17 - 2y)(3x - 17 - 2y).

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Accepted Answer

We need to simplify (3x + 17 - 2y)(3x - 17 - 2y).

Step 1: Rewrite the expression as (3x - 2y + 17)(3x - 2y - 17).

Step 2: Recognize this as a product of two binomials of the form (A + B)(A - B) = A^2 - B^2, where A = (3x - 2y) and B = 17.

Step 3: Calculate A^2 = (3x - 2y)^2 = (3x)^2 - 2*3x*2y + (2y)^2 = 9x^2 - 12xy + 4y^2.

Step 4: Calculate B^2 = 17^2 = 289.

Step 5: Apply the formula: (A + B)(A - B) = A^2 - B^2 = 9x^2 - 12xy + 4y^2 - 289.

Therefore, the simplified expression is 9x^2 - 12xy + 4y^2 - 289.

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