(a-2).jpeg "(a+3)(a-2)")
Expanding (a + 3)(a - 2)
This expression represents the product of two binomials: (a + 3) and (a - 2). To expand it, we can use the FOIL method, which stands for First, Outer, Inner, Last.
Here's how it works:
1. First: Multiply the first terms of each binomial:
- a * a = a²
2. Outer: Multiply the outer terms of the binomials:
- a * -2 = -2a
3. Inner: Multiply the inner terms of the binomials:
- 3 * a = 3a
4. Last: Multiply the last terms of each binomial:
- 3 * -2 = -6
Now, we combine the terms:
a² - 2a + 3a - 6
Finally, simplify by combining like terms:
a² + a - 6
Therefore, the expanded form of (a + 3)(a - 2) is a² + a - 6.
Other methods for expanding:
While the FOIL method is commonly used for expanding binomials, you can also use the distributive property:
- (a + 3)(a - 2) = a(a - 2) + 3(a - 2)
Then, distribute each term:
- a(a - 2) + 3(a - 2) = a² - 2a + 3a - 6
This again leads to the same simplified result: a² + a - 6.
Conclusion
Expanding expressions like (a + 3)(a - 2) is crucial for simplifying algebraic expressions and solving equations. The FOIL method provides a systematic approach, while the distributive property offers an alternative way to achieve the same result.