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Expanding the Expression (x+4)(x+9)
In mathematics, expanding an expression means writing it in a simpler form without parentheses. Let's take a look at how to expand the expression (x+4)(x+9):
Using the FOIL Method
The FOIL method is a mnemonic device used to remember the steps for multiplying two binomials. It stands for First, Outer, Inner, Last.
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * 9 = 9x
- Inner: Multiply the inner terms of the binomials: 4 * x = 4x
- Last: Multiply the last terms of each binomial: 4 * 9 = 36
Now, combine all the terms: x² + 9x + 4x + 36
Finally, simplify by combining like terms: x² + 13x + 36
Therefore, the expanded form of (x+4)(x+9) is x² + 13x + 36.
Using the Distributive Property
Another way to expand the expression is to use the distributive property. This involves multiplying each term in the first binomial by each term in the second binomial.
- Multiply (x+4) by x: x(x+4) = x² + 4x
- Multiply (x+4) by 9: 9(x+4) = 9x + 36
Now, combine the results from both steps: x² + 4x + 9x + 36
Finally, simplify by combining like terms: x² + 13x + 36
As you can see, both methods lead to the same result: x² + 13x + 36.
It's up to you to choose the method that feels most comfortable and efficient for you.