Factor 1-xy-20x^2y^2

Problem

1−x*y−20*x2*y2

Solution

1. Identify the expression as a quadratic in terms of the product x*y Let u=x*y to see the structure 1−u−20*u2

2. Rearrange the terms into the standard quadratic form a*u2+b*u+c to make factoring easier.

−20*(x*y)2−x*y+1

3. Find two numbers that multiply to a*c=(−20)*(1)=−20 and add to b=−1 These numbers are −5 and 4

4. Split the middle term −x*y using the numbers found in the previous step.

1−5*x*y+4*x*y−20*x2*y2

5. Factor by grouping the first two terms and the last two terms.

(1−5*x*y)+4*x*y*(1−5*x*y)

6. Factor out the common binomial (1−5*x*y)

(1−5*x*y)*(1+4*x*y)

Final Answer

1−x*y−20*x2*y2=(1−5*x*y)*(1+4*x*y)

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