Factoring: Sum or Difference of Two Cubes

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Multiple Choice

Complete the formula
a³-b³=

• (a-b)(a²+ab+b²)
• (a+b)(a²-ab+b²)
• (a-b)(a²-ab+b²)
• (a+b)(a²+ab+b²)

Multiple Choice

The pattern

$$x^3-y^3$$  is called a/an _________.

• Difference of Two Squares

• Sum of Two Cubes

• Difference of Two Cubes

• Square of a Binomial

Multiple Choice

The binomial 

$$x^3+y^3$$ is called a/an _________.

• Difference of Two Squares

• Sum of Two Cubes

• Difference of Two Cubes

• Square of a Binomial

Multiple Choice

To use factoring the difference of two cubes, rewrite the expression  $$m^6-n^6$$  to  $$\left(m^2\right)^3-$$ _________. 

• $$\left(n^2\right)^3$$  

• $$\left(n^3\right)^2$$  

• $$2\left(n^3\right)^{ }$$  

• $$3\left(n^2\right)^{ }$$  

Multiple Choice

Factoring the sum or difference of two cubes can be used ONLY if the two terms of the binomials have perfect square roots.

• TRUE

• FALSE

Multiple Choice

Factor completely $$64x^6+y^6$$

• $$\left(4x^2+y^2\right)\left(16x^4-4x^2y^2-y^4\right)$$  

• $$\left(4x^2-y^2\right)\left(16x^4+4x^2y^2+y^4\right)$$  

• $$\left(4x^2+y^2\right)\left(16x^4-4x^2y^2+y^4\right)$$  

• $$\left(4x^2-y^2\right)\left(16x^4-4x^2y^2-y^4\right)$$  

Multiple Choice

Factor $$27x^3-64$$  

• $$\left(3x+4\right)\left(9x^2-12x+16\right)$$  

• $$\left(3x+4\right)\left(9x^2+12x+16\right)$$  

• $$\left(3x-4\right)\left(9x^2-12x+16\right)$$  

• $$\left(3x-4\right)\left(9x^2+12x+16\right)$$  

Multiple Choice

Which of the following is the complete factored form of $$x^3y^9+1000$$  

• $$\left(xy^3+10\right)\left(x^2y^6-10xy^3+100\right)$$  

• $$\left(xy^{ }+10\right)\left(x^2y^2-10xy^{ }+100\right)$$  

• $$\left(xy^3-10\right)\left(x^2y^6+10xy^3+100\right)$$  

• $$\left(xy^3-10\right)\left(x^2y^6-20xy^3+100\right)$$  

Multiple Choice

What must be multiplied to $$\left(5x^2+2y\right)$$  to get a product of  $$125x^6+8y^3$$  ?

• $$\left(5x^2+2y\right)$$  

• $$\left(5x^2-2y\right)$$  

• $$\left(5x^4+10x^2y+2y^2\right)$$  

• $$\left(25x^4-10x^2y+4y^2\right)$$  

Multiple Choice

What is ALWAYS the first step when factoring?

• Look for the GCF

• Write a, b, and c

• Difference of squares

• Use the X-Puzzle

Multiple Choice

Which number is both a perfect square and a perfect cube?

• 64

• 27

• 81

• 16

Multiple Choice

Complete the formula

a³+b³=

• (a-b)(a²+ab+b²)

• (a+b)(a²-ab+b²)

• (a-b)(a²-ab+b²)

• (a+b)(a²+ab+b²)

Multiple Choice

Factor:   x³ + 1

• (x + 1)³
• (x+1)(x² - x + 1)
• (x - 1) (x² + x - 1)
• (x + 1)(x² - 2x + 1)

Multiple Choice

Factor: 8x³ - 1

• (2x - 1)(4x² + 2x + 1)
• (2x + 1)(4x² - 2x + 1)
• (2x - 1)(4x² - 2x - 1)
• (2x + 1)(4x² +2x + 1)

Multiple Choice

Factor
27x³-64

• (3x-4)(9x²+12x+16)
• (3x-4)(9x²-12x+16)
• (3x+4)(9x²-12x+16)
• (3x+4)(9x²+12x+16)

Multiple Choice

Fully Factor the Following
8x³-27

• (2x+3)(4x²-6x+9)
• (2x-3)(4x²+6x+9)
• (2x-3)(4x²+6x-9)
• (2x-3)(2x²+6x+9)

Multiple Choice

Identify if the expression can be factored as sum or difference of cubes:

3x³ + 24

• No

• Yes

• Yes, getting GCF first

• It is a sum of squares

Multiple Choice

WHAT FACTORING TECHNIQUE YOU HAVE TO USE TO SOLVE FOR THE FACTORS OF 27X³-343?

• DIFFERENCE OF TWO CUBES

• DIFFERENCE OF TWO SQUARES

• FACTORING BY GCF

• SUM OF TWO CUBES

Multiple Choice

Factor 8z³+125

• (2z+5)(4z²-25)

• (2z+5)(4z²+10z+25)

• (2z+5)(4z²-10z+25)

• 4z+5)(2z²-5z+25)

Multiple Choice

Factor this difference of cubes:
x³ - 343

• (x + 7) (x² - 7x + 49)
• (x² + 1) (x - 343)
• (x - 7) (x² + 7x + 49)
• (x² - 343) (x + 1)

Draw

Factor completely $$3x^3+375y^6$$