Factor (2x-3)^3(x+1)+(x-3)(2x-3)^2

Problem

(2*x−3)3*(x+1)+(x−3)*(2*x−3)2

Solution

1. Identify the greatest common factor between the two terms, which is (2*x−3)2

2. Factor out (2*x−3)2 from the entire expression.

(2*x−3)2*[(2*x−3)*(x+1)+(x−3)]

3. Expand the product (2*x−3)*(x+1) inside the brackets using the FOIL method.

(2*x−3)2*[2*x2+2*x−3*x−3+x−3]

4. Combine like terms within the brackets.

(2*x−3)2*[2*x2+(2*x−3*x+x)+(−3−3)]

(2*x−3)2*[2*x2+0*x−6]

5. Simplify the expression inside the brackets.

(2*x−3)2*(2*x2−6)

6. Factor out the constant 2 from the second binomial.

2*(2*x−3)2*(x2−3)

Final Answer

(2*x−3)3*(x+1)+(x−3)*(2*x−3)2=2*(2*x−3)2*(x2−3)

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