Factoring Special Products: Quadratics

According to your formula chart, what is the formula for factoring a "Difference of Squares"?

• a² - b² = (a-b)(a+b)

• a² - 2ab + b² = (a-b)²

Answer explanation

These are some examples of a "difference of squares":

x^2 - 49

25x^2 - 16

81x^2 - 144

They are all "missing" the x-term, or linear term, in the middle because they had exact opposite values and zeroed out. For example:

(x-7)(x+7)

x^2 + 7x - 7x - 49

x^2 - 49

Tags

CCSS.HSA.APR.C.4

According to your formula chart, what is the formula for factoring a "Perfect Square Trinomial" that has a negative coefficient on the middle term?

• a² - b² = (a-b)(a+b)

• a² - 2ab + b² = (a-b)²

Answer explanation

These are examples of perfect square trinomials with a negative coefficient on the middle term:

x^2 - 14x + 49

9x^2 - 6x + 1

Their factored forms are:

(x-7)^2

(3x-1)^2

NEVER DISTRIBUTE THE EXPONENT! Always use formula or expand and multiply (a.k.a. FOIL or box).

Tags

CCSS.HSA.APR.C.4

According to your formula chart, what is the formula for factoring a "Perfect Square Trinomial" that has a positive coefficient on the middle term?

• a² - b² = (a-b)(a+b)

• a² + 2ab + b² = (a+b)²

• a² - 2ab + b² = (a-b)²

Answer explanation

These are examples of perfect square trinomials with a positive coefficient on the middle term:

x^2 + 10x + 25

4x^2 + 12x + 9

Their factored forms are:

(x+5)^2

(2x+3)^2

NEVER DISTRIBUTE THE EXPONENT! Always use formula or expand and multiply (a.k.a. FOIL or box).

Tags

CCSS.HSA.APR.C.4

Select BOTH of the PERFECT SQUARE TRINOMIALS.

Hint, the formulas are:

a² + 2ab + b² = (a+b)²

and

a² - 2ab + b² = (a-b)²

• x² - 6x + 9

• r² + 12r + 36

• x² + 16x + 100

• r² - 9r + 49

Tags

CCSS.HSA.APR.C.4

Factor the perfect square trinomial:

9x² + 6x + 1

• (3x)² + (1)²

• (3x - 1)²

• (3x + 1)²

• (x + 3)²

Tags

CCSS.HSA.APR.C.4

Factor the perfect square trinomial:

x² - 10x + 25

• (x)² - (5)²

• (x - 5)²

• -(x + 5)²

• (-5x + 5)²

Tags

CCSS.HSA.APR.C.4

Factor the difference of squares:

x² - 100

_{(If using the number puzzle to factor, think about what the "b" value is... Otherwise, use your formula chart.)}

• (x-10)(x+10)

• (x-10)²

• (x+10)²

Answer explanation

When the expression has a subtraction sign between two perfect squares, a^2 - b^2, you can take the square root of each term and set up the factors like this:

(a-b)(a+b)

So, x^2 - 100 becomes

(x-10)(x+10).

Tags

CCSS.HSA.APR.C.4

Factor the difference of squares:

9x² - 16

_{(If using the number puzzle to factor, think about what the "b" value is... Otherwise, use your formula chart.)}

• (3x-4)(3x+4)

• (3x-4)²

• (3x+4)²

Answer explanation

When the expression has a subtraction sign between two perfect squares, a^2 - b^2, you can take the square root of each term and set up the factors like this:

(a-b)(a+b)

So, 9x^2 - 16 becomes

(3x-4)(3x+4).

Tags

CCSS.HSA.APR.C.4

Select ALL of the non-factorable, or "prime" expressions.

• x² - 50

• m² + 16

• n² + 6n + 3

• u² - 144

What are the factors of 81m² - 1 ?