Algebra: Difference of Two Squares

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Questions and Answers

What does the difference of two squares identity require to be applied?

Two squared terms subtracted from each other. (correct)
Two squared terms divided by each other.
Two squared terms added to each other.
Two squared terms multiplied together.

What is the correct factored form of the expression $a^2 - b^2$?

(a + b)(a - b)
(a + b)(a + b)
(a - b)(a - b)
(a - b)(a + b) (correct)

Which scenario is NOT a use of the difference of two squares?

Applying concepts in coordinate geometry.
Finding the roots of quadratic equations.
Solving a system of linear equations. (correct)
Simplifying algebraic expressions.

In recognizing patterns for applying the difference of two squares, which of the following indicates that the technique can be used?

<p>Presence of perfect square terms and subtraction between them. (B)</p> Signup and view all the answers

What is one key benefit of understanding the difference of two squares in algebra?

<p>It simplifies the process of factoring expressions. (D)</p> Signup and view all the answers

Flashcards

Difference of Two Squares

A mathematical identity that states the difference of two squared terms can be factored into the product of two binomials, one with addition and one with subtraction.

Perfect Square

A number that can result from squaring an integer (e.g., 9 is a perfect square because 3 x 3 = 9).

Factoring

Expressing an algebraic expression as a product of two or more factors (e.g., x² - 4 can be factored into (x + 2)(x - 2)).

Identity (in algebra)

An algebraic expression that simplifies to a constant value regardless of the values of the variables (e.g., (a+b)(a-b) = a² - b²).

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Applications of the Difference of Two Squares

The difference of two squares can be applied to simplify algebraic expressions, solve equations by factoring, and solve problems in coordinate geometry.

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Study Notes

Difference of Two Squares

This identity applies to expressions with two squared terms subtracted.
For example, x² - 9 can be rewritten as (x)² - (3)² .
The expression can be factored into two binomials: one with addition and one with subtraction.
For instance, x² - 9 factors to (x + 3)(x - 3) .
This identity is used to simplify algebraic expressions.
It aids in solving equations through factoring.
It's applicable in coordinate geometry and problem-solving.
Recognize perfect squares when using this identity (e.g., 25x²).
Ensure subtraction exists between the squared terms.