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You are watching: Factor 8x^3-27

Factoring and Perfect Cubes cg-tower.com Topical rundown | Algebra 2 overview | MathBits" Teacher resources Terms the Use call Person: Donna Roberts
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In Algebra 1, you functioned with factoring the differenceof 2 perfect squares. a2 - b2 = (a - b)(a + b)

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The sum of two perfect squares, a2 + b2, 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.


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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.)
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If girlfriend remember the the very first part of the factoring (the binomial part) is the sum (or difference) the 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 "b" in your recognized pattern. For example, if you know: a3 + b3 = (a + b)(a2 - ab + b2) Replace b with -b: a3 + (-b)3 = (a + (-b))(a2 - a(-b) + (-b)2) and friend have: a3 - b3 = (a - b)(a2 + ab + b2) Let"s check out that this formulas room actually true.


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When working through perfect cubes look for: perfect cube numerical values: 8, 27, 64, 125, 216, 343, 512, ... Powers for perfect cube algebraic values:
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Is this expression the difference of perfect cubes? Look for perfect cubes and appropriate powers. 8x3 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.


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once you job-related with the Binomial Theorem, friend will get a much better understandingof the sample of the coefficients in these formulas. 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