2.jpeg "(2x+3y+5)2")
Expanding (2x + 3y + 5)²
The expression (2x + 3y + 5)² represents the square of a trinomial, which means multiplying the trinomial by itself.
There are a couple of ways to approach this problem:
1. Using the FOIL Method
The FOIL method is a common technique for multiplying binomials. However, it can be extended to trinomials by systematically multiplying each term in the first trinomial by each term in the second trinomial.
- First: (2x * 2x) = 4x²
- Outer: (2x * 3y) = 6xy
- Inner: (2x * 5) = 10x
- Last: (3y * 2x) = 6xy
- Outer: (3y * 3y) = 9y²
- Inner: (3y * 5) = 15y
- Last: (5 * 2x) = 10x
- Outer: (5 * 3y) = 15y
- Last: (5 * 5) = 25
Combining like terms, we get: 4x² + 12xy + 20x + 9y² + 30y + 25
2. Using the Square of a Sum Formula
The formula (a + b + c)² = a² + b² + c² + 2ab + 2ac + 2bc can be used to directly expand the expression.
- a = 2x
- b = 3y
- c = 5
Substituting these values into the formula, we get:
(2x)² + (3y)² + 5² + 2(2x)(3y) + 2(2x)(5) + 2(3y)(5)
Simplifying, we get the same result as before: 4x² + 12xy + 20x + 9y² + 30y + 25
Therefore, the expanded form of (2x + 3y + 5)² is 4x² + 12xy + 20x + 9y² + 30y + 25.