(a%2B4).jpeg "(5a+2)(a+4)")
Expanding the Expression (5a + 2)(a + 4)
This article will explore how to expand the expression (5a + 2)(a + 4) using the FOIL method.
Understanding the FOIL Method
The FOIL method is a mnemonic acronym used to remember the steps for expanding the product of two binomials:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of the binomials.
- Inner: Multiply the inner terms of the binomials.
- Last: Multiply the last terms of each binomial.
Expanding the Expression
Let's apply the FOIL method to (5a + 2)(a + 4):
- First: (5a)(a) = 5a²
- Outer: (5a)(4) = 20a
- Inner: (2)(a) = 2a
- Last: (2)(4) = 8
Now, we combine the results:
5a² + 20a + 2a + 8
Finally, simplify by combining like terms:
5a² + 22a + 8
Therefore, the expanded form of (5a + 2)(a + 4) is 5a² + 22a + 8.
Conclusion
By applying the FOIL method, we can successfully expand the expression (5a + 2)(a + 4) into a simplified polynomial form. This method provides a structured approach for multiplying binomials, ensuring that all terms are accounted for.