2-answer.jpeg "(5a+6b)2 Answer")
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 First, Outer, Inner, Last.
- 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.