Math Problem Statement

(2x+2)(x-9)

Solution

To expand the expression (2x+2)(x9)(2x + 2)(x - 9), we will apply the distributive property (also known as the FOIL method for binomials).

  1. First, multiply the first terms:
    2x×x=2x22x \times x = 2x^2

  2. Next, multiply the outer terms:
    2x×9=18x2x \times -9 = -18x

  3. Then, multiply the inner terms:
    2×x=2x2 \times x = 2x

  4. Finally, multiply the last terms:
    2×9=182 \times -9 = -18

Now, combine all these terms together:
2x218x+2x182x^2 - 18x + 2x - 18

Combine like terms:
2x216x182x^2 - 16x - 18

So, the expanded form of (2x+2)(x9)(2x + 2)(x - 9) is: 2x216x182x^2 - 16x - 18

Would you like more details or further explanation?

Here are 5 related questions you might want to consider:

  1. How do you factor quadratic expressions like 2x216x182x^2 - 16x - 18?
  2. What are the solutions to 2x216x18=02x^2 - 16x - 18 = 0?
  3. Can you simplify (2x+2)(x9)(2x + 2)(x - 9) further if given specific values of xx?
  4. How does the distributive property work with trinomials?
  5. What happens when you apply the FOIL method to different types of binomials?

Tip: Always combine like terms after distributing to simplify your expression fully!

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Math Problem Analysis

Mathematical Concepts

Algebra
Distributive Property
Binomials

Formulas

(a+b)(c+d) = ac + ad + bc + bd
Combining like terms

Theorems

Distributive Property of Multiplication over Addition

Suitable Grade Level

Grades 8-10