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Simplifying the Expression (a + b)² + (a - b)²
This article will guide you through the process of simplifying the algebraic expression (a + b)² + (a - b)². We will use the FOIL method and some algebraic rules to achieve the simplified form.
Understanding the Expression
The expression involves squaring two binomials, (a + b) and (a - b). To simplify, we need to expand these squares using the FOIL method:
First: Multiply the first terms of each binomial. Outer: Multiply the outer terms of the binomials. Inner: Multiply the inner terms of the binomials. Last: Multiply the last terms of each binomial.
Expanding the Squares
Let's expand each square:
(a + b)² = (a + b)(a + b) = a² + ab + ab + b² = a² + 2ab + b²
(a - b)² = (a - b)(a - b) = a² - ab - ab + b² = a² - 2ab + b²
Combining the Expanded Terms
Now, let's substitute these expanded forms back into the original expression:
**(a + b)² + (a - b)² = (a² + 2ab + b²) + (a² - 2ab + b²) **
Simplifying the Expression
Finally, we combine like terms:
- a² + a² = 2a²
- 2ab - 2ab = 0
- b² + b² = 2b²
Therefore, the simplified form of the expression is: 2a² + 2b²
Conclusion
By using the FOIL method and combining like terms, we have successfully simplified the expression (a + b)² + (a - b)² to 2a² + 2b². This simplification can be useful for various algebraic manipulations and problem-solving in mathematics.