Final answer:
In mathematics, the word 'Operation' fits the pattern 'O_e_a_i_n' and refers to the process of expanding double brackets using the distributive property, such as the FOIL method to multiply two binomials together.
Step-by-step explanation:
The math-related word that fits the pattern 'O_e_a_i_n' and is associated with expanding double brackets is Operation. In mathematics, an operation is a process or action that is carried out to solve a problem. Specifically, when we talk about expanding double brackets, we're referring to the process of applying the distributive property to multiply two binomials together. This involves multiplying each term in the first bracket by each term in the second bracket.
For example, if we want to expand (x + 3)(x + 2), we would use the FOIL method (which stands for First, Outer, Inner, Last) as follows:
- Multiply the first terms: x * x = x^2
- Multiply the outer terms: x * 2 = 2x
- Multiply the inner terms: 3 * x = 3x
- Multiply the last terms: 3 * 2 = 6
We then combine like terms:
x^2 + 2x + 3x + 6 = x^2 + 5x + 6
This is the expanded form of the original expression with double brackets. This process is a key operation in algebra, particularly when simplifying expressions and solving equations.