Math Problem Statement

(2x−1)(x+9)

Solution

Let's expand the expression (2x1)(x+9)(2x−1)(x+9) using the distributive property (also known as the FOIL method for binomials).

(2x1)(x+9)=2x(x+9)1(x+9)(2x - 1)(x + 9) = 2x(x + 9) - 1(x + 9)

Now distribute each term:

=2xx+2x91x19= 2x \cdot x + 2x \cdot 9 - 1 \cdot x - 1 \cdot 9

Simplifying each multiplication:

=2x2+18xx9= 2x^2 + 18x - x - 9

Now combine like terms:

=2x2+17x9= 2x^2 + 17x - 9

So, the expanded form of (2x1)(x+9)(2x−1)(x+9) is:

2x2+17x92x^2 + 17x - 9

Would you like more details or have any questions?

Here are 5 related questions you might consider:

  1. How do you factor quadratic expressions like 2x2+17x92x^2 + 17x - 9?
  2. What is the solution to the equation 2x2+17x9=02x^2 + 17x - 9 = 0?
  3. How would you apply the distributive property to a trinomial?
  4. Can you explain how to simplify like terms in polynomial expressions?
  5. How do you identify the coefficients in a quadratic expression?

Tip: Always organize your terms by powers of xx to ensure clarity when simplifying expressions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Expansion
Distributive Property

Formulas

(a+b)(c+d) = ac + ad + bc + bd
FOIL method for binomials

Theorems

Distributive Property

Suitable Grade Level

Grades 7-9