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Expanding the Expression (x+5)(x+3)
In mathematics, expanding an expression means multiplying out all the terms to simplify it. In this case, we have the expression (x+5)(x+3). To expand this, we can use the FOIL method (First, Outer, Inner, Last).
Using the FOIL Method
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * 3 = 3x
- Inner: Multiply the inner terms of the binomials: 5 * x = 5x
- Last: Multiply the last terms of each binomial: 5 * 3 = 15
Now, we have: x² + 3x + 5x + 15
Simplifying the Expression
Finally, combine the like terms: x² + 8x + 15
Therefore, the expanded form of (x+5)(x+3) is x² + 8x + 15.
Additional Notes
- This expanded form is a quadratic expression, meaning it has a highest power of x as 2.
- You can use this expanded form to solve for the values of x that make the original expression equal to zero. This is often called finding the roots of the equation.
- The FOIL method is a helpful tool for expanding binomials, but it's important to understand the underlying principle of multiplying each term in one binomial by each term in the other binomial.