(2-3a).jpeg "(2+3a)(2-3a)")
Expanding the Expression (2+3a)(2-3a)
This expression is a special case of multiplication known as the difference of squares. Let's explore how to expand it and understand why it's called that.
Understanding the Difference of Squares
The difference of squares pattern states:
(a + b)(a - b) = a² - b²
In our case, we have:
- a = 2
- b = 3a
Expanding the Expression
Applying the difference of squares pattern, we get:
(2 + 3a)(2 - 3a) = 2² - (3a)²
Simplifying:
(2 + 3a)(2 - 3a) = 4 - 9a²
Key Points
- The difference of squares pattern allows us to quickly expand expressions like this.
- The result is always a difference of two perfect squares.
- This pattern is useful for factoring expressions and solving equations.
Example Application
Let's say we want to find the value of (2 + 3a)(2 - 3a) when a = 1.
We can simply substitute a = 1 into our expanded expression:
4 - 9(1)² = 4 - 9 = -5
Therefore, when a = 1, the value of (2 + 3a)(2 - 3a) is -5.