Factor (3x+2)^2+8(3x+2)+12

Problem

(3*x+2)2+8*(3*x+2)+12

Solution

1. Identify a common structure in the expression by letting a variable represent the repeated linear term. Let u=3*x+2

2. Substitute u into the original expression to create a standard quadratic trinomial.

(u)2+8*(u)+12

3. Factor the quadratic trinomial by finding two numbers that multiply to 12 and add to 8 These numbers are 6 and 2

(u+6)*(u+2)

4. Substitute back the original expression 3*x+2 in place of u

((3*x+2)+6)*((3*x+2)+2)

5. Simplify the terms inside each set of parentheses by combining the constants.

(3*x+8)*(3*x+4)

Final Answer

(3*x+2)2+8*(3*x+2)+12=(3*x+8)*(3*x+4)

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