Math Problem Statement

(x+6)(x-2)

Solution

To solve (x+6)(x2)(x + 6)(x - 2), we can expand the expression using the distributive property (also known as FOIL for binomials). Here's the step-by-step process:

(x+6)(x2)=x(x2)+6(x2)(x + 6)(x - 2) = x(x - 2) + 6(x - 2)

Now, let's distribute:

x(x2)=x22xx(x - 2) = x^2 - 2x 6(x2)=6x126(x - 2) = 6x - 12

Now, add the two results together:

x22x+6x12x^2 - 2x + 6x - 12

Combine like terms:

x2+4x12x^2 + 4x - 12

Thus, the expanded form of (x+6)(x2)(x + 6)(x - 2) is:

x2+4x12x^2 + 4x - 12

Would you like further details on any part of this process?


Here are 5 related questions to expand on this:

  1. How do you factor quadratic expressions like x2+4x12x^2 + 4x - 12?
  2. Can you solve the equation (x+6)(x2)=0(x + 6)(x - 2) = 0?
  3. What are the roots of the quadratic equation x2+4x12=0x^2 + 4x - 12 = 0?
  4. How do you complete the square for an equation like x2+4x12x^2 + 4x - 12?
  5. What is the vertex form of the quadratic equation x2+4x12x^2 + 4x - 12?

Tip: Always combine like terms after distributing to simplify expressions properly.

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Math Problem Analysis

Mathematical Concepts

Algebra
Binomial Expansion
Quadratic Expressions

Formulas

Distributive Property: a(b + c) = ab + ac

Theorems

Distributive Law

Suitable Grade Level

Grades 8-10