Question

Factor each expression. $$ a^{2}-49 $$

Name: Problem 25, Chapter 8: Algebra 1 Common Core
Uploaded: 2020-04-02T20:42:11-08:00
Duration: 42 s
Channel: Cory Kuzinski
Description: Factor each expression. a^2-49

   Factor each expression.
$$
a^{2}-49
$$

Algebra 1 Common Core

Randall I.… 1st Edition

Chapter 8, Problem 25

Instant Answer

Solved by Expert Cory Kuzinski

04/02/2020

Step 1

The difference of squares is a term used when you have two perfect squares separated by a subtraction sign. In this case, $a^{2}$ and $49$ are perfect squares. Show more…

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Factor each expression. $$ a^{2}-49 $$

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Key Concepts

Polynomial Factoring

Polynomial factoring is the broader concept of expressing a polynomial as a product of simpler polynomials or factors. This technique simplifies polynomial expressions, aids in solving polynomial equations, and is foundational for further algebraic manipulations.

Difference of Squares

The difference of squares is a key algebraic pattern where an expression takes the form x² - y². This pattern factors neatly into (x - y)(x + y), making it a powerful tool for simplifying and solving quadratic expressions. Recognizing this form helps in quickly breaking down expressions into binomial factors.

Identifying Perfect Squares

Identifying perfect squares is crucial for applying the difference of squares formula. A term is a perfect square if it can be written as another term squared. Recognizing that both a² and 49 (which is 7²) are perfect squares is essential to applying the correct factorization method.

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