(x-3).jpeg "(4x-5)(x-3)")
Expanding (4x-5)(x-3)
This article will walk you through the process of expanding the expression (4x-5)(x-3). This involves multiplying two binomials, which is a common task in algebra.
Understanding the Process
Expanding the expression means we need to multiply each term in the first binomial by each term in the second binomial. This can be done using the FOIL method:
- 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.
Applying FOIL
- First: (4x) * (x) = 4x²
- Outer: (4x) * (-3) = -12x
- Inner: (-5) * (x) = -5x
- Last: (-5) * (-3) = 15
Combining Like Terms
After multiplying, we have: 4x² - 12x - 5x + 15
Combine the like terms (-12x and -5x):
4x² - 17x + 15
Final Result
Therefore, the expanded form of (4x-5)(x-3) is 4x² - 17x + 15.
Conclusion
Expanding expressions like (4x-5)(x-3) is a fundamental skill in algebra. By understanding and applying the FOIL method, you can successfully multiply binomials and simplify expressions.