Math Problem Statement

3x(2x - y + 2)

Solution

The expression provided is:

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

Let's simplify it step by step using the distributive property:

  1. Multiply each term inside the parentheses by 3x3x: 3x×2x=6x23x \times 2x = 6x^2 3x×(y)=3xy3x \times (-y) = -3xy 3x×2=6x3x \times 2 = 6x

  2. Combine all the terms: 6x23xy+6x6x^2 - 3xy + 6x

So, the simplified expression is:

6x23xy+6x6x^2 - 3xy + 6x

Would you like more details on any of the steps, or do you have any questions?

Here are five related questions to explore:

  1. How would this expression change if y=0y = 0?
  2. What happens if x=1x = 1 in the simplified expression?
  3. Can you factor out any common terms from the final expression?
  4. What would the result be if you substituted specific values for both xx and yy?
  5. How would the process change if the expression included a division instead of multiplication?

Tip: When distributing, always ensure each term inside the parentheses is multiplied by the factor outside.

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Math Problem Analysis

Mathematical Concepts

Algebra
Distributive Property
Simplifying Expressions

Formulas

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

Theorems

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Suitable Grade Level

Grades 7-9