(x-4).jpeg "(2x-3)(x-4)")
Expanding and Simplifying (2x - 3)(x - 4)
This expression represents the product of two binomials. To simplify it, we need to expand it using the distributive property (also known as FOIL).
FOIL stands for First, Outer, Inner, Last and helps us remember the steps involved in multiplying 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.
Let's apply this to our expression:
(2x - 3)(x - 4)
- First: (2x) * (x) = 2x²
- Outer: (2x) * (-4) = -8x
- Inner: (-3) * (x) = -3x
- Last: (-3) * (-4) = 12
Now, we combine all the terms:
2x² - 8x - 3x + 12
Finally, we simplify by combining like terms:
2x² - 11x + 12
Therefore, the simplified form of (2x - 3)(x - 4) is 2x² - 11x + 12.
Additional Notes:
- This expanded expression represents a quadratic equation.
- You can factor this quadratic equation back into the original binomials: (2x - 3)(x - 4)
- This expansion can be useful for various applications, such as solving equations, finding roots, and graphing quadratic functions.