Factoring: Difference of Two Squares

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Multiple Choice

What is ALWAYS the first step when factoring?

• Look for the GCMF

• Write a, b, and c

• Difference of squares

• Group

Multiple Choice

Factor 4x²-9

• (4x-9)(4x+9)

• (2x-3)(2x+3)

• 2x-3

• (2x-4.5)(2x+4.5)

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

3x² - 75

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

Multiple Choice

16p³ - 81q⁶

• (4p + 9q) (4p - 9q)
• (4p² + 9q³) (4p - 9q³)
• (4p² + 9q) (4p - 9q)
• Can't factor using Diff. of Squares

Multiple Choice

r⁴ - q⁴

• (r² + q²) (r² - q²)
• (r² - q²) (r² - q²)
• (r + q) (r - q)
• Can't factor using Diff. of Squares

Multiple Choice

9n² + 1

• (3n + 1) (3n - 1)
• (3n - 1) (3n - 1)
• (n + 3) (n - 3)
• Can't factor using Diff. of Squares

Multiple Choice

r² - 9t²

• (r + 3t) (r - 3t)
• (r - 3t) (r - 3t)
• (3r + t) (3r - t)
• Can't factor using Diff. of Squares

Multiple Choice

36x² - 64

• (6x - 8)(6x + 8)
• 4(3x - 4)(3x + 4)
• Not Factorable
• (9x - 16)(9x + 16)

Multiple Choice

Which of these can factor using difference of two squares?

• 144x² - 49y²

• x² + 4x - 12

• 100x² + 20x + 1

• 14x - 16

Multiple Choice

Which one is false about the difference of two squares?

• We can factor because there is addition sign.

• We can factor because there is a perfect squared number (Example: x², 25, 49)

• Formula: a² - b² = (a + b) (a - b)

• We can factor because there is minus sign.

Multiple Choice

We can't factor using difference of two square this

49x² + 4y². Why?

• Because 4 is not a perfect cubed number.

• Because 4 is not a perfect squared number.

• Because 49 is not a perfect squared number.

• Because we can't factor using difference of two squares if it is addition sign.

Multiple Choice

49n² - 25

• Not Factorable
• (3n + 5)(3n - 5)
• (7n + 5)(7n - 5)
• (5n + 7)(5n - 7)

Multiple Choice

In ( $$x^2$$ - 100 ) is equal to ( x + 10 ) and

• ( x + 10)

• ( x - 10)

• x

• 10

Fill in the Blank

( 4x² - 4 ) = ( 2x - 2 ) ( 2x + ___)

Multiple Select

If the area of your garden is ( d^{2 _} 16 ) and the length is

( d + 4) , what is the width?

• ( d+ 2)

• ( d - 2)

• ( d + 4)

• (d - 4)

Multiple Choice

x² - 400

• ( x - 200) ( x + 200) 
• ( x + 20) ( x + 20) 
• Prime
• ( x - 20) ( x + 20) 

Multiple Choice

We can't factor using difference of two square this

25x² - 51y². Why?

• Because 51 is not a perfect cubed number.

• Because 51 is not a perfect squared number.

• Because 25 is not a perfect squared number.

• Because we can't factor using difference of two squares if it is addition sign.

Multiple Choice

Which of the following is NOT a perfect square?

• 1

• 4

• 100

• 8

​Aristotle

​"Pleasure in the job puts perfection in the work."