Factor 12x^2-27

Problem

12*x2−27

Solution

1. Identify the greatest common factor (GCF) for the terms 12*x2 and 27 which is 3

2. Factor out the GCF from the expression.

3*(4*x2−9)

3. Recognize that the expression inside the parentheses, 4*x2−9 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=3

3*((2*x)2−3)

5. Rewrite the expression in its completely factored form.

3*(2*x−3)*(2*x+3)

Final Answer

12*x2−27=3*(2*x−3)*(2*x+3)

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