AA Notes 4.3: Factoring Sums & Differences of Cubes

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Presentation transcript:

AA Notes 4.3: Factoring Sums & Differences of Cubes Objectives • Define “cubes” • Factor Sums of Cubes • Factor Difference of Cubes

Concept: What are Perfect Cubes? Something times something times something. Where the something is a factor 3 times. Example: 2  2  2 = 8, so 8 is a perfect cube. x2  x2  x2 = x6 so x6 is a perfect cube. It is easy to see if a variable is a perfect cube. Just see if the exponent is divisible by 3.

Concept: What Is A Sum or Difference of Cubes Has two terms The terms are separated by a + or – sign Each term is a perfect cube The sum or difference of two cubes will factor into a binomial  trinomial.

Concept: Factoring Sums of Cubes same sign always opposite always +

Concept: Factoring Differences of Cubes same sign Sum of Cubes always opposite always + Difference of Cubes

Concept: Factoring Sums & Differences of Cubes Now we know how to get the signs, let’s work on what goes inside. Square this term to get this term. Cube root of 1st term Product of cube root of 1st term and cube root of 2nd term. Cube root of 2nd term

You did it! Concept: Factoring Sums & Differences of Cubes cont… 3x 5 Factor this Difference of Cubes. Watch your signs!!! 3x 5 9x2 15x 25 Cube root of 1st term Multiply these to get this. Square this term to get this term. Cube root of 2nd term Square this term to get this term. You did it! I hope you took notes because we are done here!!!

Factoring Sums & Differences of Cubes Example 2: Factor each of the following polynomials 8x3 – 27 = (2x – 3)((2x)2 + (2x)(3) + (3)2)  Use the pattern a3 – b3 = (a – b)(a2 + ab + b2) = (2x – 3)(4x2 + 6x + 9) b) 9x4 – 9x = 9x(x3 – 1)  First remove the GCF = 9x(x – 1)(x2 + x + 1)  Factor the difference of cubes x3 – 1

Homework Time