Factor 15x^2-16xy+4y^2

Problem

15*x2−16*x*y+4*y2

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x*y+c*y2 where a=15 b=−16 and c=4

2. Find two numbers that multiply to a⋅c=15⋅4=60 and add to b=−16

3. Determine the factors of 60 that satisfy the condition, which are −10 and −6

4. Rewrite the middle term −16*x*y using these two numbers as −10*x*y−6*x*y

5. Group the terms into two pairs: (15*x2−10*x*y)+(−6*x*y+4*y2)

6. Factor out the greatest common factor from each pair: 5*x*(3*x−2*y)−2*y*(3*x−2*y)

7. Factor out the common binomial (3*x−2*y) to obtain the final factored form.

Final Answer

15*x2−16*x*y+4*y2=(5*x−2*y)*(3*x−2*y)

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