Math Problem Statement

Simplify the algebraic expression 6(x + 9y).

Solution

The expression in the image is:

6(x+9y)6(x + 9y)

To simplify this, we apply the distributive property:

6(x+9y)=6x+69y=6x+54y6(x + 9y) = 6 \cdot x + 6 \cdot 9y = 6x + 54y

So, the simplified expression is:

6x+54y6x + 54y

Would you like any further clarification?

Here are five related questions to further explore this concept:

  1. How would the expression change if you multiplied by a different constant, like 3 instead of 6?
  2. What happens if you apply the distributive property to three terms inside the parentheses?
  3. How do you factor an expression like 6x+54y6x + 54y back to its original form?
  4. Can you apply the distributive property to expressions with subtraction, like 5(a4b)5(a - 4b)?
  5. How would this process differ for more complex expressions involving exponents?

Tip: The distributive property is useful in algebra for simplifying expressions and solving equations. Always remember to distribute the factor to each term inside the parentheses.

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Math Problem Analysis

Mathematical Concepts

Algebra
Distributive Property

Formulas

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

Theorems

Distributive Property

Suitable Grade Level

Grades 6-8