Factor (a+b)^2-(a-b)^2

Problem

(a+b)2−(a−b)2

Solution

1. Identify the expression as a difference of squares, which follows the pattern x2−y2=(x−y)*(x+y)

2. Assign the variables such that x=(a+b) and y=(a−b)

3. Substitute these values into the difference of squares formula:

((a+b)−(a−b))*((a+b)+(a−b))

4. Simplify the terms inside the first set of parentheses by distributing the negative sign:

(a+b−a+b)

2*b

5. Simplify the terms inside the second set of parentheses:

(a+b+a−b)

2*a

6. Multiply the resulting simplified terms together:

(2*b)*(2*a)

4*a*b

Final Answer

(a+b)2−(a−b)2=4*a*b

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