(2x%2B3).jpeg "(2x+3)(2x+3)")
Expanding (2x+3)(2x+3)
This expression represents the product of two identical binomials: (2x+3) and (2x+3). There are two common methods to expand this:
1. Using the FOIL Method
FOIL stands for First, Outer, Inner, Last, and helps us remember to multiply each term of the first binomial by each term of the second.
- First: (2x) * (2x) = 4x²
- Outer: (2x) * (3) = 6x
- Inner: (3) * (2x) = 6x
- Last: (3) * (3) = 9
Combining the terms, we get: 4x² + 6x + 6x + 9
Finally, simplify by combining like terms: 4x² + 12x + 9
2. Using the Square of a Binomial Pattern
The expression (2x+3)(2x+3) is simply the square of the binomial (2x+3). The square of a binomial pattern states:
(a + b)² = a² + 2ab + b²
Applying this to our expression, we have:
- a = 2x
- b = 3
Substituting into the pattern:
(2x)² + 2(2x)(3) + 3²
Expanding and simplifying:
4x² + 12x + 9
Conclusion
Both methods lead to the same result: 4x² + 12x + 9. The choice of method depends on your preference and the complexity of the expression. Understanding the square of a binomial pattern is particularly useful for more complex expressions.