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**Factoring and Perfect Cubes**cg-tower.com Topical rundown | Algebra 2 overview | MathBits" Teacher resources

**Terms the Use call Person:**Donna Roberts

In Algebra 1, you functioned with factoring the **difference**of 2 perfect **squares.** *a*2 - *b*2 = (*a - b*)(*a + b*)

*The sum of two perfect squares,*

*a*2 +

*b*2, does

**not**aspect under real numbers.

In Algebra 2, us will extend our factoring skills to factoring** both** the **difference **and the **sum **of two perfect **cubes**.

as soon as trying come remember this patterns, remember the the an initial binomial ax in the factored form in every pattern keeps the same sign as the sign in between the perfect cubes. The sign separating the first and second terms the the trinomial is the contrary the sign in between the perfect cubes, and also the last authorize in the trinomial is always positive. (Note the each formula has only one negative sign in the solution.) |

*a*and

*b*, friend can always find the remainder of the factored answer by using long division.

One much more idea because that remembering this patterns: If you remember **one** the the patterns, you can acquire the other pattern by substituting "* -b*" in location of "

*" in your recognized pattern. For example, if you know:*

**b***a*3 +

*b*3 = (

*a*+

*b*)(

*a*2 -

*ab + b*2) Replace

*b*with

*-b*:

*a*3 + (

*-b*)3 = (

*a*+ (-

*b*))(

*a*2

*- a*(

*-b*)

*+*(

*-b*)2)

*and friend have:*

*a*3 -

*b*3 = (

*a*-

*b*)(

*a*2

*+ ab + b*2)

*Let"s check out that this formulas room actually true.*

When working through perfect cubes look for: perfect cube numerical values: 8, 27, 64, 125, 216, 343, 512, ... Powers for perfect cube algebraic values: Is this expression the difference of perfect cubes? Look for perfect cubes and appropriate powers. 8 x3 and 27 space perfect cubes: 8x3 = (2x)3 and also 27 = 33 So, yes, this is the distinction of perfect cubes. At very first glance, this might not look like the distinction of perfect cubes. BUT, if we factor out the typical factor the 7, we will discover a hidden distinction of perfect cubes.See more: How Long Is 80 Inches Equals How Many Feet, 80 In To Ft 80 Inches To Feet |

*Remember:*you can always find these fads by just multiplying(

*x*+

*a*)3 = (

*x + a*)(

*x + a*)(

*x + a*)(

*x*-

*a*)3 = (

*x - a*)(

*x - a*)(

*x - a*)

Topical overview | Algebra 2 synopsis | cg-tower.com | MathBits" Teacher resources Terms of Use** call Person:** Donna Roberts