Math Problem Statement

(N-7)(n+6)

Solution

The expression you've provided is (n7)(n+6)(n - 7)(n + 6). This is a product of two binomials and can be expanded using the distributive property, often referred to as the FOIL method (First, Outer, Inner, Last).

Solution:

Let's expand the expression:

(n7)(n+6)(n - 7)(n + 6)

  1. First: Multiply the first terms in each binomial: n×n=n2n \times n = n^2

  2. Outer: Multiply the outer terms: n×6=6nn \times 6 = 6n

  3. Inner: Multiply the inner terms: 7×n=7n-7 \times n = -7n

  4. Last: Multiply the last terms: 7×6=42-7 \times 6 = -42

Now, combine all these results:

n2+6n7n42n^2 + 6n - 7n - 42

Finally, combine like terms:

n2n42n^2 - n - 42

So, the expanded form of (n7)(n+6)(n - 7)(n + 6) is n2n42n^2 - n - 42.

Would you like more details or have any questions?

Related Questions:

  1. How do you factor the expression n2n42n^2 - n - 42 back into its binomial form?
  2. What is the significance of the FOIL method in expanding binomials?
  3. Can you apply the distributive property to a trinomial multiplied by a binomial?
  4. How do you solve the equation n2n42=0n^2 - n - 42 = 0?
  5. What are some common mistakes to avoid when expanding binomials?

Tip: When expanding binomials, carefully combine like terms to ensure accuracy. This step is crucial, especially when dealing with more complex expressions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Binomial Expansion

Formulas

FOIL Method

Theorems

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Suitable Grade Level

Grades 7-9