Factor (x+y-6)(x-y-6)

Problem

(x+y−6)*(x−y−6)

Solution

1. Rearrange the terms inside each set of parentheses to group x and −6 together.

((x−6)+y)*((x−6)−y)

2. Identify the pattern as a difference of squares, which follows the form (a+b)*(a−b)=a2−b2

a=x−6

b=y

3. Apply the formula for the difference of squares.

(x−6)2−y2

4. Expand the squared binomial (x−6)2 using the identity (a−b)2=a2−2*a*b+b2

x2−12*x+36−y2

5. Reorder the terms into standard polynomial form.

x2−y2−12*x+36

Final Answer

(x+y−6)*(x−y−6)=x2−y2−12*x+36

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