Difference of Squares

Front

What is the Difference of Squares formula?

Back

The Difference of Squares formula states that a² - b² = (a - b)(a + b).

Front

How do you factor a difference of squares expression?

Back

To factor a difference of squares expression, identify a and b in the form a² - b², then apply the formula (a - b)(a + b).

Front

What is the result of factoring 25x² - 81?

Back

(5x - 9)(5x + 9) because 25x² is a perfect square and 81 is also a perfect square.

Front

Is x² + 81 a difference of squares?

Back

No, x² + 81 is not a difference of squares; it is a sum of squares and cannot be factored over the real numbers.

Front

What are the factors of 4w² - 49?

Back

(2w - 7)(2w + 7) because it follows the difference of squares pattern.

Front

How do you identify a difference of squares in an expression?

Back

Look for two perfect squares separated by a subtraction sign, such as a² - b².

Front

What is the factored form of 81 - 25w²?

Back

(9 - 5w)(9 + 5w) because it is a difference of squares.

Front

Can the expression 16r² - 196 be factored using the difference of squares?

Back

Yes, it can be factored as (4r - 14)(4r + 14).

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer.

Front

What is the significance of the difference of squares in algebra?

Back

It provides a method for factoring certain quadratic expressions, simplifying calculations and solving equations.