Let's simplify the given expression step by step:

The expression is:

\[
4x(2x - y) - 3y(5y + (-4xy)) - (5x - 2y)
\]

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

1. **First Term**: 
   \[
   4x(2x - y) = 4x \cdot 2x - 4x \cdot y = 8x^2 - 4xy
   \]

2. **Second Term**:
   \[
   -3y(5y + (-4xy)) = -3y \cdot 5y + (-3y) \cdot (-4xy) = -15y^2 + 12xy^2
   \]

3. **Third Term**:
   \[
   -(5x - 2y) = -5x + 2y
   \]

### Step 2: Combine all the terms together:
\[
8x^2 - 4xy - 15y^2 + 12xy^2 - 5x + 2y
\]

### Step 3: Final expression (since there are no like terms to combine):
\[
8x^2 - 4xy - 15y^2 + 12xy^2 - 5x + 2y
\]

Thus, the simplified form of the expression is:
\[
8x^2 - 4xy - 15y^2 + 12xy^2 - 5x + 2y
\]

Would you like further details or clarifications?

Here are 5 questions related to this:

1. How do you factor polynomials like \(8x^2 - 4xy\)?
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.

Explore how to simplify the algebraic expression 4x(2x - y) - 3y(5y - 4xy) - (5x - 2y) using the distributive property and combining like terms. This step-by-step solution covers core algebraic concepts suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation