Sum and Difference of Cubes

Sum & Difference of Cubes

Slide: 1

Sum of Cubes A sum of two cubed terms, x3 + y3, can be factored as: (x + y)(x2 – xy + y2)

Factor the following expression: 8a3 + 125b3

8a3 + 125b3 can be rewritten as (2a)3 + (5b)3 Using the sum of cubes rule:

8a3 + 125b3 = (2a)3 + (5b)3 = (2a + 5b)[(2a)2 – (2a)(5b) + (5b)2] = (2a + 5b)(4a2 – 10ab + 25b2)

Slide: 2

Difference of Cubes A difference between two cubed terms, x3 – y3, can be factored as: (x – y)(x2 + xy + y2)

Factor the following expression: 64p3 – 27q3

64p3 – 27q3 can be rewritten as (4p)3 – (3q)3 Using the difference of cubes rule:

64p3 – 27q3 = (4p)3 – (3q)3 = (4p – 3q)[(4p)2 + (4p)(3q) + (3q)2] = (4p – 3q)(16p2 + 12pq + 9q2)

Slide: 3

Factor the following expression completely: 1 + 1,000a3

Slide: 4

Factor the following expression completely: 2x2z9 – 432x5y3

Slide: 5