(x-4).jpeg "(x-10)(x-4)")
Expanding (x-10)(x-4)
In algebra, we often encounter expressions like (x-10)(x-4) and need to expand them. This means writing it in a simpler form without the parentheses. Here's how to do it:
The FOIL Method
The most common method to expand this type of expression is the FOIL method. 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 to our expression (x-10)(x-4):
- First: x * x = x²
- Outer: x * -4 = -4x
- Inner: -10 * x = -10x
- Last: -10 * -4 = 40
Now we have: x² - 4x - 10x + 40
Combining Like Terms
Finally, we combine the terms with the same variable and exponent:
x² - 14x + 40
Therefore, the expanded form of (x-10)(x-4) is x² - 14x + 40.
Additional Notes
- You can also use the distributive property to expand the expression.
- The FOIL method is a shortcut that works for multiplying two binomials.
- Remember that expanding the expression doesn't change its value, it just changes its form.
Hopefully, this explanation helps you understand how to expand expressions like (x-10)(x-4)!