(x+4)(x+7) Answer

2 min read Jun 16, 2024
(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:

  1. First: (x) * (x) =
  2. Outer: (x) * (7) = 7x
  3. Inner: (4) * (x) = 4x
  4. 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.

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