(x%2B7)-answer.jpeg "(x+4)(x+7) Answer")
Expanding the Expression: (x+4)(x+7)
This article will walk you through the steps involved in expanding the expression (x+4)(x+7). This process is fundamental in algebra and helps us understand how to manipulate and simplify expressions.
The FOIL Method
The FOIL method provides a systematic way to expand expressions of this form. FOIL stands for:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of the binomials.
- Inner: Multiply the inner terms of the binomials.
- Last: Multiply the last terms of each binomial.
Let's apply FOIL to our expression:
- First: (x) * (x) = x²
- Outer: (x) * (7) = 7x
- Inner: (4) * (x) = 4x
- Last: (4) * (7) = 28
Now we combine the terms:
x² + 7x + 4x + 28
Simplifying the Expression
Finally, we simplify by combining the like terms (the terms with 'x'):
x² + 11x + 28
Conclusion
Therefore, the expanded form of (x+4)(x+7) is x² + 11x + 28. Understanding how to expand binomials like this is crucial for solving algebraic equations and understanding various mathematical concepts.