Factor x^2+4xy-12y^2

Problem

x2+4*x*y−12*y2

Solution

1. Identify the expression as a quadratic trinomial in the form a*x2+b*x*y+c*y2 where a=1 b=4 and c=−12

2. Find two numbers that multiply to the product of the first and last coefficients (1×−12=−12 and add up to the middle coefficient (4.

3. Determine the factors of −12 that satisfy these conditions, which are 6 and −2 since 6×−2=−12 and 6 + (-2) = 4$.

4. Write the binomial factors using these numbers, including the variable y in the second term of each binomial.

Final Answer

x2+4*x*y−12*y2=(x+6*y)*(x−2*y)

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