Diference+and+Sum+of+Cubes

= Difference and Sum of Cubes = These are the basic equations used in finding the difference and sum of cubes. It is important to remember that the first symbol in the second bracket is opposite to the symbol at the start of the equation (if its x - y then it will be a + in brackets) x 3 - y 3 = (x - y)(x 2 + xy + y 2 ) x 3 + y 3 = (x + y)(x 2 - xy + y 2 )

Ex. 1: 8z3 - 27 = (2z) 3 - 3 3 (2z - 3)(4z 2 - 6z + 9) Ex 2: q6 + 1/64 = (q 2 ) 3 + (1/4) 3 (q 2 + 1/4)( (q 2 ) 2 - 1/4q 2 +(1/4) 2 ) (q 2 + 1/4)( q 4 - q 2 /4 + 1/16) Ex 3: 125x6 - 8/x3 = (5x 2 ) 3 - (2/x) 3 (5x 2 - 2/x)( (5x 2 ) 2 + 5x 2 (2/x) + (2/x) 2 ) (5x 2 - 2/x)(25x 4 + 10x + 4/x 2 )