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Q.
- Expand using distributive property: To prove the identity , we will expand the right-hand side of the equation using the distributive property (also known as the FOIL method for binomials).
- Multiply first terms: First, we multiply the first terms of each binomial: .
- Multiply outer terms: Next, we multiply the outer terms: .
- Multiply inner terms: Then, we multiply the inner terms: .
- Multiply last terms: Finally, we multiply the last terms of each binomial: .
- Combine all products: Now, we combine all the products: .
- Cancel out additive inverses: We notice that and are additive inverses, so they cancel each other out: .
- Simplify the expression: Simplifying the expression, we are left with , which is the left-hand side of the original equation.
