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Expanding the Expression (x+3)(x+8)
This expression represents the multiplication of two binomials: (x+3) and (x+8). To expand it, we can use the FOIL method (First, Outer, Inner, Last):
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * 8 = 8x
- Inner: Multiply the inner terms of the binomials: 3 * x = 3x
- Last: Multiply the last terms of each binomial: 3 * 8 = 24
Now, combine the terms: x² + 8x + 3x + 24
Finally, simplify by combining the like terms: x² + 11x + 24
Therefore, the expanded form of (x+3)(x+8) is x² + 11x + 24.
Understanding the FOIL Method
The FOIL method is a simple and visual way to remember how to multiply two binomials. It ensures that we multiply each term in the first binomial by each term in the second binomial.
Other Approaches
While the FOIL method is commonly used, you can also use the distributive property to expand the expression:
- Distribute (x+3) over (x+8): (x+3) * (x+8) = x(x+8) + 3(x+8)
- Distribute again: x² + 8x + 3x + 24
- Simplify: x² + 11x + 24
Applications
Understanding how to expand binomials like (x+3)(x+8) is essential for various mathematical concepts, including:
- Factoring quadratic expressions
- Solving quadratic equations
- Graphing quadratic functions
- Solving problems in algebra and calculus
By mastering this skill, you can tackle more complex mathematical problems with confidence.