Free Printable FACTORING POLYNOMIALS - Sum or Difference of Two Cubes

1.

The pattern

x^3-y^3

is called a/an _________.

a)

Difference of Two Squares

b)

Sum of Two Cubes

c)

Difference of Two Cubes

d)

Square of a Binomial

2.

The binomial

x^3+y^3

is called a/an _________.

a)

Difference of Two Squares

b)

Sum of Two Cubes

c)

Difference of Two Cubes

d)

Square of a Binomial

3.

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

a)

$\left(m^2\right)^3$

b)

$\left(m^3\right)^2$

c)

$2\left(m^3\right)^{ }$

d)

$3\left(m^2\right)^{ }$

4.

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

a)

TRUE

b)

FALSE

5.

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

a)

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

b)

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

c)

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

d)

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

6.

To get the cube root of a variable with exponent, divide the exponent by three and raise it to the same base.

a)

TRUE

b)

FALSE

7.

Factor $27x^3-64$

a)

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

b)

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

c)

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

d)

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

8.

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

a)

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

b)

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

c)

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

d)

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

9.

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

a)

$\left(5x^2+2y\right)$

b)

$\left(5x^2-2y\right)$

c)

$\left(5x^4+10x^2y+2y^2\right)$

d)

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

10.

Complete the formula
a³-b³=

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

FACTORING POLYNOMIALS - Sum or Difference of Two Cubes

Total questions: 10

Worksheet time: 5mins

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