Factor x^2+8xy+15y^2

Problem

x2+8*x*y+15*y2

Solution

1. Identify the expression as a quadratic trinomial in the form a*x2+b*x*y+c*y2 where a=1 b=8 and c=15

2. Find two numbers that multiply to the constant term c=15 and add to the middle coefficient b=8

3. Determine that the numbers are 3 and 5 because 3⋅5=15 and 3 + 5 = 8$.

4. Write the factored form using these two numbers as coefficients for the y terms within the binomial factors.

Final Answer

x2+8*x*y+15*y2=(x+3*y)*(x+5*y)

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