Math Problem Statement

(x+2y).(3x-y)=

Solution

To simplify the expression (x+2y)(3xy)(x + 2y)(3x - y), we apply the distributive property (also known as FOIL for binomials):

(x+2y)(3xy)=x(3xy)+2y(3xy)(x + 2y)(3x - y) = x(3x - y) + 2y(3x - y)

Now expand each term:

  1. x(3xy)=3x2xyx(3x - y) = 3x^2 - xy
  2. 2y(3xy)=6xy2y22y(3x - y) = 6xy - 2y^2

Combine the results:

3x2xy+6xy2y23x^2 - xy + 6xy - 2y^2

Simplify the like terms (xy+6xy=5xy-xy + 6xy = 5xy):

3x2+5xy2y23x^2 + 5xy - 2y^2

Thus, the simplified expression is:

3x2+5xy2y2\boxed{3x^2 + 5xy - 2y^2}

Would you like a detailed breakdown of each step?


Related Questions:

  1. How is the distributive property used in binomial multiplication?
  2. What are like terms, and how do you combine them?
  3. How would this change if the second binomial were (3x+y)(3x + y)?
  4. Can this expression be factored further?
  5. How does this relate to the geometry of a parabola?

Tip:

Always simplify like terms step by step to avoid errors, especially when working with multiple variables.

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Math Problem Analysis

Mathematical Concepts

Algebra
Binomial Multiplication
Polynomial Simplification

Formulas

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

Theorems

Distributive Property

Suitable Grade Level

Grades 8-10