(x%2B4).jpeg "(x+7)(x+4)")
Expanding (x+7)(x+4)
In mathematics, we often encounter expressions like (x+7)(x+4). This is a product of two binomials, and we can expand it using the FOIL method. FOIL stands for First, Outer, Inner, Last, which refers to the order in which we multiply the terms:
1. First: Multiply the first terms of each binomial: x * x = x²
2. Outer: Multiply the outer terms of the binomials: x * 4 = 4x
3. Inner: Multiply the inner terms of the binomials: 7 * x = 7x
4. Last: Multiply the last terms of each binomial: 7 * 4 = 28
Now, we combine all the terms:
x² + 4x + 7x + 28
Finally, we combine the like terms (the terms with 'x' in them):
x² + 11x + 28
Therefore, the expanded form of (x+7)(x+4) is x² + 11x + 28.
Why is expanding binomials important?
Expanding binomials is a crucial step in many mathematical operations, including:
- Solving quadratic equations: Quadratic equations involve expressions like x² + 11x + 28, which can be factored into the original binomial form (x+7)(x+4).
- Simplifying expressions: Expanding binomials can simplify complex expressions, making them easier to work with.
- Graphing functions: Expanding binomials can help us understand the shape and behavior of quadratic functions.
By understanding how to expand binomials, we gain a fundamental understanding of algebraic manipulation, which is essential for solving a wide range of mathematical problems.