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).

Tags

CCSS.HSA.APR.C.4

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.

Tags

CCSS.HSA.APR.C.4

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.

Tags

CCSS.8.EE.A.2

Front

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

Back

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

Tags

CCSS.HSA.APR.C.4

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.

Tags

CCSS.HSA.APR.C.4

Front

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

Back

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

Tags

CCSS.HSA.APR.C.4

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).

Tags

CCSS.HSA.APR.C.4

Front

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

Back

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

Tags

CCSS.HSA.APR.C.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.

Tags

CCSS.HSA.APR.C.4

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.

Tags

CCSS.6.EE.A.3