Problem 237 Factor completely. $$ 121 r^... [FREE SOLUTION]

Chapter 6: Problem 237

Factor completely. $$ 121 r^{2}-s^{2} $$

Short Answer

Expert verified

(11r + s)(11r - s)

Step by step solution

- Recognize the Difference of Squares

The given expression is of the form $a^2 - b^2$, which can be factored using the difference of squares formula: $a^2 - b^2 = (a + b)(a - b)$

- Identify the Terms

Identify $a$ and $b$ in the expression. In the given expression $121r^2 - s^2$, $a^2 = 121r^2$ and $b^2 = s^2$. Therefore, $a = 11r$ and $b = s$.

- Apply the Difference of Squares Formula

Substitute $a = 11r$ and $b = s$ into the difference of squares formula: $121r^2 - s^2 = (11r + s)(11r - s)$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

difference of squares

A 'difference of squares' is a specific type of algebraic expression. It follows the pattern of one term squared minus another term squared, written as $a^2 - b^2$. This kind of expression can be factored into two binomials. The formula for factoring the difference of squares is simple: $a^2 - b^2 = (a + b)(a - b)$. To spot a difference of squares, ensure you have exactly two terms, both of which should be perfect squares, separated by a minus sign.

algebraic expressions

Algebraic expressions are mathematical phrases that can include numbers, variables, and operation symbols. For example, $121r^2 - s^2$ is an algebraic expression.
These expressions are like the building blocks of algebra. They can be simplified, factored, and solved based on specific algebraic rules.
In our exercise, we've used the algebraic expression $121r^2 - s^2$ and identified it as a difference of squares so we can factor it.

factoring techniques

Factoring techniques are methods used to rewrite algebraic expressions as a product of simpler factors. This exercise emphasizes the 'difference of squares' technique.
To factor $121r^2 - s^2$, follow these steps:
- Identify the perfect squares within the expression: $121r^2$ and $s^2$.
- Recognize the expression as a difference of squares: $a^2 - b^2$.
- Apply the formula: $a^2 - b^2 = (a + b)(a - b)$.
- Substitute $a = 11r $ and $b = s $ to get: $ (11r + s)(11r - s) $.
Factoring is a crucial skill in algebra, helping to simplify expressions and solve equations more easily.

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91影视

Factor completely. $$ 121 r^{2}-s^{2} $$

Short Answer

Step by step solution

- Recognize the Difference of Squares

- Identify the Terms

- Apply the Difference of Squares Formula

Key Concepts

difference of squares

algebraic expressions

factoring techniques

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