(8a-5).jpeg "(2a-1)(8a-5)")
Expanding the Expression (2a-1)(8a-5)
This article will guide you through the process of expanding the algebraic expression (2a-1)(8a-5). This involves using the distributive property, also known as FOIL (First, Outer, Inner, Last).
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. In the context of our expression, this means:
(2a - 1)(8a - 5) = 2a(8a - 5) - 1(8a - 5)
Applying FOIL
FOIL is a mnemonic device that helps remember the order of multiplying terms when expanding expressions:
- First: Multiply the first terms of each binomial: 2a * 8a = 16a²
- Outer: Multiply the outer terms of the binomials: 2a * -5 = -10a
- Inner: Multiply the inner terms of the binomials: -1 * 8a = -8a
- Last: Multiply the last terms of each binomial: -1 * -5 = 5
Combining Like Terms
Now, we have: 16a² - 10a - 8a + 5
Combining the like terms (-10a and -8a): 16a² - 18a + 5
Final Result
Therefore, the expanded form of (2a - 1)(8a - 5) is 16a² - 18a + 5.