## 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:

**F**irst: Multiply the first terms of each binomial.
**O**uter: Multiply the outer terms of the binomials.
**I**nner: Multiply the inner terms of the binomials.
**L**ast: 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.