Math Problem Statement

4x(2x-y)-3y(5y+-4xy)-(5x-2y)

Solution

Let's simplify the given expression step by step:

The expression is:

4x(2xy)3y(5y+(4xy))(5x2y)4x(2x - y) - 3y(5y + (-4xy)) - (5x - 2y)

Step 1: Distribute the terms inside each group of parentheses.

  1. First Term: 4x(2xy)=4x2x4xy=8x24xy4x(2x - y) = 4x \cdot 2x - 4x \cdot y = 8x^2 - 4xy

  2. Second Term: 3y(5y+(4xy))=3y5y+(3y)(4xy)=15y2+12xy2-3y(5y + (-4xy)) = -3y \cdot 5y + (-3y) \cdot (-4xy) = -15y^2 + 12xy^2

  3. Third Term: (5x2y)=5x+2y-(5x - 2y) = -5x + 2y

Step 2: Combine all the terms together:

8x24xy15y2+12xy25x+2y8x^2 - 4xy - 15y^2 + 12xy^2 - 5x + 2y

Step 3: Final expression (since there are no like terms to combine):

8x24xy15y2+12xy25x+2y8x^2 - 4xy - 15y^2 + 12xy^2 - 5x + 2y

Thus, the simplified form of the expression is: 8x24xy15y2+12xy25x+2y8x^2 - 4xy - 15y^2 + 12xy^2 - 5x + 2y

Would you like further details or clarifications?

Here are 5 questions related to this:

  1. How do you factor polynomials like 8x24xy8x^2 - 4xy?
  2. How can the distributive property simplify more complex equations?
  3. What are the steps for combining like terms in an expression?
  4. Can you simplify the expression further by grouping terms differently?
  5. How do you solve an equation after simplifying the expression?

Tip: Always check for common factors in each term when simplifying expressions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplifying Expressions
Distributive Property
Combining Like Terms

Formulas

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

Theorems

Distributive Law
Associative Law of Addition

Suitable Grade Level

Grades 8-10