Simplify (a+b)(a-b)

Problem

(a+b)*(a−b)

Solution

1. Identify the expression as a product of two binomials in the form of a sum and a difference.

2. Apply the FOIL method to multiply the terms: First, Outer, Inner, Last.

3. Multiply the First terms: a⋅a=a2

4. Multiply the Outer terms: a⋅(−b)=−a*b

5. Multiply the Inner terms: b⋅a=a*b

6. Multiply the Last terms: b⋅(−b)=−b2

7. Combine the results into a single expression: a2−a*b+a*b−b2

8. Simplify by canceling the middle terms −a*b and a*b as they sum to zero.

Final Answer

(a+b)*(a−b)=a2−b2

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