Factor y^4(y+2)^3+y^5(y+2)^4

Problem

y^4*(y+2)^3+y^5*(y+2)^4

Solution

1. Identify the greatest common factor (GCF) between the two terms by looking at the powers of y and the powers of the binomial (y+2)

2. Determine the lowest power for each common base, which is y^4 and (y+2)^3

3. Factor out the GCF y^4*(y+2)^3 from both terms of the expression.

4. Simplify the remaining expression inside the brackets by combining like terms.

5. Distribute the y into the binomial (y+2) in the second term to get y^2+2*y

6. Combine the terms inside the brackets to reach the final factored form.

Final Answer

y^4*(y+2)^3+y^5*(y+2)^4=y^4*(y+2)^3*(1+y^2+2*y)

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