Difference of Two Squares

Front

What is the difference of two squares?

Back

The difference of two squares is a special factoring technique that applies to expressions of the form a^2 - b^2, which can be factored into (a + b)(a - b).

Front

Can you factor 16x^3 - 25y^2 using the difference of two squares? Why or why not?

Back

No, because 16x^3 is not a perfect square. The difference of two squares can only be applied to expressions where both terms are perfect squares.

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer or a variable. For example, 1, 4, 9, 16, and x^2 are perfect squares.

Front

Factor the expression x^2 - 9 using the difference of two squares.

Back

The expression can be factored as (x + 3)(x - 3).

Front

Why can't you factor 49x^2 + 4y^2 using the difference of two squares?

Back

You cannot factor it because it contains an addition sign. The difference of two squares only applies to expressions with a subtraction sign.

Front

Factor the expression 4y^2 - 9 using the difference of two squares.

Back

The expression can be factored as (2y + 3)(2y - 3).

Front

What is the general form of the difference of two squares?

Back

The general form is a^2 - b^2 = (a + b)(a - b).

Front

Can the expression x^2 - 16 be factored? If so, how?

Back

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

Front

What is the first step in factoring a difference of two squares?

Back

Identify if both terms are perfect squares and if the expression is in the form a^2 - b^2.

Front

What happens if an expression has more than two terms when trying to apply the difference of two squares?

Back

The difference of two squares cannot be applied directly; you may need to simplify or rearrange the expression first.