## Expanding the Expression (5a + 6b)²

In algebra, expanding an expression means writing it in a simpler form, usually without parentheses. This is done by applying the distributive property and combining like terms. Let's look at how to expand the expression (5a + 6b)².

**Understanding the Basics**

(5a + 6b)² is the same as (5a + 6b)(5a + 6b). To expand this, we need to multiply each term in the first set of parentheses by each term in the second set of parentheses.

**The Steps**

**FOIL Method:**A helpful acronym for remembering the order of multiplication is**F**irst,**O**uter,**I**nner,**L**ast.**First:**5a * 5a = 25a²**Outer:**5a * 6b = 30ab**Inner:**6b * 5a = 30ab**Last:**6b * 6b = 36b²

**Combine Like Terms:**Notice that the outer and inner terms are both 30ab. We can combine them: 25a² + 30ab + 30ab + 36b² = 25a² + 60ab + 36b²

**The Result**

Therefore, the expanded form of (5a + 6b)² is **25a² + 60ab + 36b²**.

**Key Points**

**Squaring an expression means multiplying it by itself.****The FOIL method helps remember the steps of multiplying binomials.****Always combine like terms for the final simplified expression.**

Understanding how to expand expressions like (5a + 6b)² is crucial in solving various algebraic problems. It also helps in understanding other mathematical concepts like factorization and quadratic equations.