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Expanding (x+6)(x+9)
In mathematics, expanding an expression means multiplying out all the terms. To expand the expression (x+6)(x+9), we can use the FOIL method:
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: 6 * x = 6x Last: Multiply the last terms of each binomial: 6 * 9 = 54
Now we have: x² + 9x + 6x + 54
Finally, combine the like terms: x² + 15x + 54
Therefore, the expanded form of (x+6)(x+9) is x² + 15x + 54.
Understanding the FOIL Method
The FOIL method is a helpful mnemonic device for remembering the steps involved in multiplying two binomials. It ensures that you multiply every term in the first binomial by every term in the second binomial.
Other Methods for Expanding
While the FOIL method is a common approach, you can also expand this expression using other methods:
- Distributive Property: Distribute each term in the first binomial over the second binomial.
- Box Method: Create a grid with the terms of each binomial on the top and side and multiply to fill in the boxes.
Regardless of the method you choose, the expanded form of (x+6)(x+9) will always be x² + 15x + 54.