(x%5E2-3x)-foil-method.jpeg "(x+5)(x^2-3x) Foil Method")
Using the FOIL Method to Expand (x+5)(x^2 - 3x)
The FOIL method is a handy acronym that helps us remember the steps for multiplying two binomials. It stands for:
- 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.
Let's apply this method to expand the expression (x+5)(x^2 - 3x):
Step 1: First
- Multiply the first terms of each binomial: x * x^2 = x^3
Step 2: Outer
- Multiply the outer terms of the binomials: x * -3x = -3x^2
Step 3: Inner
- Multiply the inner terms of the binomials: 5 * x^2 = 5x^2
Step 4: Last
- Multiply the last terms of the binomials: 5 * -3x = -15x
Step 5: Combine like terms
Now we have: x^3 - 3x^2 + 5x^2 - 15x
Combining like terms gives us: x^3 + 2x^2 - 15x
Therefore, the expanded form of (x+5)(x^2 - 3x) is x^3 + 2x^2 - 15x.
Key Points:
- The FOIL method is a systematic way to multiply binomials.
- Remember to combine like terms after applying the FOIL method.
- This method is a fundamental concept in algebra, and it's essential to understand it for solving various equations and expressions.