Factor Difference Special Products

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).

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

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

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).

Factor.

4x² - 64

• Prime

• ( 2x - 32) (2 x + 32)

• ( 2x - 8) (2 x - 8)

• (2x - 8) (2x + 8)

Multiply:
(r + 7)(r − 7)

• r ² − 49 

• r ² + 14

• r ² − 7r + 49 

• r − 49

Factor 49r²-36

• (7r + 6)(7r - 6)

• (7r + 6)(7r + 6)

• (7r - 6)(7r - 6)

Factor: x² - 4x + 4

• (x + 2)²

• (x - 2)²

• (x + 4)²

• (x - 4)²

Factor

x² + 18x + 81

• (x + 9)(x – 9)

• (x + 18)²

• (x + 9)²

• (x + 6)²