Math Problem Statement

Solve

Factor the expression 49 - 81x^2.

Solution

The expression shown in the image is:

4981x249 - 81x^2

This is a difference of squares. The general form of the difference of squares is:

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

Let's identify aa and bb in the expression:

  • 4949 is 727^2, so a=7a = 7.
  • 81x281x^2 is (9x)2(9x)^2, so b=9xb = 9x.

Applying the difference of squares formula:

4981x2=(79x)(7+9x)49 - 81x^2 = (7 - 9x)(7 + 9x)

Therefore, the factored form of 4981x249 - 81x^2 is:

(79x)(7+9x)(7 - 9x)(7 + 9x)

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

  1. How do you identify if an expression is a difference of squares?
  2. Can the difference of squares be applied if one of the terms is not a perfect square?
  3. What is the factored form of 16x22516x^2 - 25?
  4. How would you factor 100x4100 - x^4?
  5. How can you verify if your factored expression is correct?

Tip: Always check if each term in the expression is a perfect square before applying the difference of squares rule.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Factoring
Difference of Squares

Formulas

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

Theorems

Difference of Squares Theorem

Suitable Grade Level

Grades 9-12