https://file.aiquickdraw.com/mathbot/file/1728744713966ziyli6tc.jpg

To factorize the expression \( w^2 - \frac{9}{49} \) into the form \( (w + a)(w + b) \), let's follow these steps:

### Step 1: Recognize the Difference of Squares
The given expression is a difference of squares because it can be written as:
\[
w^2 - \left( \frac{3}{7} \right)^2
\]

### Step 2: Apply the Difference of Squares Formula
The difference of squares formula states that:
\[
x^2 - y^2 = (x - y)(x + y)
\]

Using this formula, we can factorize \( w^2 - \frac{9}{49} \) as follows:
\[
w^2 - \left( \frac{3}{7} \right)^2 = \left( w - \frac{3}{7} \right)\left( w + \frac{3}{7} \right)
\]

### Step 3: Identify Values of \( a \) and \( b \)
In this factorized form:
\[
(w + a)(w + b)
\]
we can see that:
\[
a = -\frac{3}{7} \quad \text{and} \quad b = \frac{3}{7}
\]

### Answer
The possible values of \( a \) and \( b \) are:
\[
a = -\frac{3}{7} \quad \text{and} \quad b = \frac{3}{7}
\]

Would you like further details or explanations on any of the steps? 

Here are some related questions you might find helpful:
1. How can the difference of squares be applied to other types of algebraic expressions?
2. What are other factorization techniques besides the difference of squares?
3. How do you factor expressions that include higher powers, like \( w^4 - \frac{16}{81} \)?
4. How can factoring help in solving quadratic equations?
5. What is the significance of having rational versus irrational values for \( a \) and \( b \) in factorization?

**Tip:** When you encounter a term in the form \( a^2 - b^2 \), try applying the difference of squares formula for quick factorization.

The expression w^2 - 9/49 can be factorized to give an expression of the form (w + a)(w + b), where a and b are integers or fractions in their simplest form. Work out possible values of a and b.

Learn how to factor the expression w^2 - 9/49 by applying the difference of squares formula. This problem covers algebraic techniques related to factoring and is suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation