(x-3)-foil.jpeg "(4x-5)(x-3) Foil")
Understanding the FOIL Method for (4x-5)(x-3)
The FOIL method is a mnemonic acronym that stands for First, Outer, Inner, Last, helping us multiply two binomials. Let's break down how to apply it to the expression (4x-5)(x-3).
Steps to Solve (4x-5)(x-3) using FOIL
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First: Multiply the first terms of each binomial:
- (4x) * (x) = 4x²
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Outer: Multiply the outer terms of the binomials:
- (4x) * (-3) = -12x
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Inner: Multiply the inner terms of the binomials:
- (-5) * (x) = -5x
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Last: Multiply the last terms of each binomial:
- (-5) * (-3) = 15
Combining the Terms
Now we have: 4x² - 12x - 5x + 15
Finally, combine the like terms: 4x² - 17x + 15
Result
Therefore, the product of (4x-5)(x-3) using the FOIL method is 4x² - 17x + 15.
Why FOIL Works
The FOIL method ensures that every term in the first binomial is multiplied by every term in the second binomial, guaranteeing a complete and accurate expansion.