Factoring sum of cubes - Factoring Polynomials

Factoring sum of cubes

Lessons

Notes:

$\bullet$ Sum of cubes: $a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2})$

$\bullet$ Difference of cubes: $a^{3} - b^{3} = (a - b)(a^{2} + ab + b^{2})$

$\bullet$ SOAP: $a^{3} \pm b^{3} = (a[same sign]b)(a^{2}[opposite sign]ab[always positive]b^{2})$

$\bullet$ Things to consider before using the difference of cubes formula:

1. Is there a 'difference' sign? Are there two cubed terms?

2. Are the terms in order? (i.e. in descending order of degrees)

3. Is the first term positive?

4. Is there a Greatest Common Factor (GCF)?

1.
Factoring Using the Sum of Cubes Formula
Factor the following expressions:
2.
Factoring Using the Sum of Cubes Formula - Extended
Factor the following expressions:
3.
Factoring Binomials with 2 variables
Factor the following expressions:
4.
First Factor the Greatest Common Factor, Then Apply the Sum of Cubes Formula
Factor the following expressions:

Factoring sum of cubes

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Lessons

Notes:

Intro Lesson

Introduction to factoring sum of cubes i. What is sum of cubes? ii. How can sum of cubes be factored?

1.

Factoring Using the Sum of Cubes Formula Factor the following expressions:

a)

x3+125x^{3} + 125x3+125

b)

x3+827x^{3} + \frac{8}{27}x3+278​

2.

Factoring Using the Sum of Cubes Formula - Extended Factor the following expressions:

a)

64x3+164x^{3} + 164x3+1

b)

125x6+8125x^{6} + 8125x6+8

3.

Factoring Binomials with 2 variables Factor the following expressions:

a)

8x6+27y98x^{6} + 27y^{9}8x6+27y9

b)

x12y6+64x^{12}y^{6} + 64x12y6+64

4.

First Factor the Greatest Common Factor, Then Apply the Sum of Cubes Formula Factor the following expressions:

a)

−x3−8-x^{3} - 8−x3−8

b)

54x3+12854x^{3} + 12854x3+128

c)

81x10y+24xy781x^{10}y + 24xy^{7}81x10y+24xy7

5.

Making a Conclusion on Factoring Binomials Overview – Factoring Binomials i. How to identify which formulas to use? ii. What are the aspects we need to consider before factoring?

Factoring sum of cubes

Don't just watch, practice makes perfect.

We have over 1850 practice questions in Algebra for you to master.

or

Introduction to factoring sum of cubes
i. What is sum of cubes?

ii. How can sum of cubes be factored?

Factoring Using the Sum of Cubes Formula
Factor the following expressions:

$x^{3} + 125$

$x^{3} + \frac{8}{27}$

Factoring Using the Sum of Cubes Formula - Extended
Factor the following expressions:

$64x^{3} + 1$

$125x^{6} + 8$

Factoring Binomials with 2 variables
Factor the following expressions:

$8x^{6} + 27y^{9}$

$x^{12}y^{6} + 64$

First Factor the Greatest Common Factor, Then Apply the Sum of Cubes Formula
Factor the following expressions:

$-x^{3} - 8$

$54x^{3} + 128$

$81x^{10}y + 24xy^{7}$

Making a Conclusion on Factoring Binomials
Overview – Factoring Binomials

i. How to identify which formulas to use?

ii. What are the aspects we need to consider before factoring?