Factor 12x^2-75

Problem

12*x2−75

Solution

1. Identify the greatest common factor (GCF) for the terms 12*x2 and 75 which is 3

2. Factor out the GCF from the expression.

3*(4*x2−25)

3. Recognize that the expression inside the parentheses, 4*x2−25 is a difference of squares.

4. Apply the formula for the difference of squares, a2−b2=(a−b)*(a+b) where a=2*x and b=5

3*((2*x)2−5)

5. Rewrite the expression in its fully factored form.

3*(2*x−5)*(2*x+5)

Final Answer

12*x2−75=3*(2*x−5)*(2*x+5)

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