Math Problem Statement

Find the greatest common factor of the following list of terms.

x cubed yx3y​,

x squared yx2y​,

and xyxy

Question content area bottom

Part 1

The greatest common factor is

Solution

To find the greatest common factor (GCF) of the given terms, we need to determine the highest power of each variable that is common across all terms.

Given terms:

  1. x3yx^3y
  2. x2yx^2y
  3. xyxy

Step 1: Identify the factors in each term:

  • x3yx^3y has factors x3x^3 and yy.
  • x2yx^2y has factors x2x^2 and yy.
  • xyxy has factors xx and yy.

Step 2: Determine the smallest power of each variable common to all terms:

  • For xx: The smallest power of xx across the terms is x1x^1.
  • For yy: The power of yy is y1y^1 in all terms.

Step 3: Multiply these factors together to find the GCF:

The greatest common factor is the product of these minimum powers:

GCF=x1y1=xy\text{GCF} = x^1 \cdot y^1 = xy

So, the greatest common factor is xyxy.

Would you like any further details on this solution? Here are five related questions that might help you explore the topic further:

  1. How do you find the greatest common factor of polynomials with more than two terms?
  2. What is the process of factoring out the greatest common factor from a polynomial?
  3. How can the concept of GCF be extended to multiple variables and more complex expressions?
  4. How does the GCF relate to simplifying algebraic fractions?
  5. How can you apply the concept of GCF to solve real-world problems involving algebraic expressions?

Tip: When finding the GCF of algebraic terms, always look for the lowest power of each variable that appears in all terms.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Polynomials
Greatest Common Factor (GCF)

Formulas

-

Theorems

-

Suitable Grade Level

Grades 7-9