Difference of Squares

GCF and Difference of Squares Intro

Steps to Factor with Difference of Squares

• Check to make sure you have a difference of squares! You should have two perfect squares separated by a subtraction sign.

• Take the square root of each term.

• Write your two factors using the rule: a²-b² = (a+b)(a-b).

Factor 121 - 4b²

Remember: a² - b² = ​(a + b)(a - b)

There terms (121​) and (4b²) are both perfect squares.

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1) The √​121 = 11

2) The √4 = 2 and √b² = b so √(4b²) = 2b

Put that all together to see​

121 - b² = (11+ 2b) (11- 2b)​

Factor 16h² - 9a²

Remember: a² - b² = ​(a + b)(a - b)

There terms (16h²​) and (9a²) are both perfect squares.

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Therefore 16h² = (4h)² because the √​16=4 and √h² = h

AND 9a² = (3a)² because √​9=3 and √a²=a

SO​

We can ​factor 16h² - 9a² to (4h + 3a)(4h-3a)

Note: Check my work​

Factor Difference of Squares

You will hear me say difference of two perfect squares a lot (just how I learned it)

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BUT the general formula is

a² - b² = ​(a + b)(a - b)

NOTES

1) Notice that it is SUBTRACTION - it only works with subtraction

2) a² and b² will be perfect squares​

-Example a² could = 16x² and b²=81 so follow the pattern.

-16x² - 81 = (4x + 9)(​4x - 9) Check my work and make sure I am right.

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Multiple Choice

Factor 9x² – 25 completely

(Write the expression as a sum)

• x(9x – 25)

• (3x + 5)(3x + 5)

• (4.5x + 5)(4.5x – 5)

• (3x + 5)(3x – 5)

Multiple Choice

   6m² + 16m

• 2(3m² + 8m)

• 2m(3m + 8)

• 2m(3m - 8m)

• not factorable

Multiple Choice

Factor Completely:

x⁴ - 16

• ( 2x - 4) ( 2x + 4)

• ( x² - 4) ( x² + 4)

• ( x² - 8) ( x² + 8)

• ( x + 2) (x - 2) ( x² + 4)

Multiple Choice

Fully Factor the Following
25x²-81

• (5x-9)²

• (5x+9)(5x-9)

• 25(x-9)²

• (9x+5)(9x-5)

Multiple Choice

9x² - 49y⁶

• ( 3x + 7y³) (3x + 7y³) 
• ( 3x - 7y³) (3x + 7y³) 
• ( 3x - 7y³) (3x - 7y³) 
• Prime

Multiple Choice

x² - 25

• ( x + 5 ) ( x - 5 ) 
• ( x - 5 ) ( x - 5 ) 
• ( x + 5 ) ( x + 5 ) 
• Prime

Multiple Choice

4x² - 25

• (2x + 5) (2x - 5)

• (2x - 5)²

• (2x + 5)²

• 2x + 5(2x - 5)

Multiple Choice

49x² - 144y²

• (7x + 16y) (7x - 16y)

• (7x + 12y)²

• (12x + 7y) (12x - 7y)

• (7x + 12y) (7x - 12y)