Math Problem Statement

solve

Factor 36 - y²

Solution

The given expression is:

36y236 - y^2

This is a difference of squares, which follows the formula:

a2b2=(ab)(a+b)a^2 - b^2 = (a - b)(a + b)

Here, we recognize:

36=62andy2=y236 = 6^2 \quad \text{and} \quad y^2 = y^2

So, applying the difference of squares formula:

36y2=(6y)(6+y)36 - y^2 = (6 - y)(6 + y)

Final Answer:

(6y)(6+y)(6 - y)(6 + y)

Would you like a more detailed explanation or have any questions?

Related Questions:

  1. How do you factor other types of quadratic expressions?
  2. What is the difference of squares rule, and when is it used?
  3. Can you give another example of factoring a difference of squares?
  4. How do you factor expressions that are not perfect squares?
  5. How can factoring be used to solve quadratic equations?

Tip:

Whenever you see a subtraction between two perfect squares, try using the difference of squares formula!

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Math Problem Analysis

Mathematical Concepts

Algebra
Factoring
Difference of Squares

Formulas

a² - b² = (a - b)(a + b)

Theorems

Difference of Squares Theorem

Suitable Grade Level

Grades 8-10