Quandaries
and Queries 

Name: larry Who is asking: Student Question: X^{ 3}  8Y^{ 3} 8X^{ 2}  72 64A^{ 3}  125B^{ 6} 

Hi Larry, There are some patterns that you need to recognize in
order to factor these expressions. These patterns are called the difference
of squares, the difference of cubes and the sum of cubes. I see them this
way Difference of squares Difference of cubes Sum of cubes Your first problem is a sum of cubes where the red patch is the letter X and the green patch is the letter Y. Lets look at the second problem, X^{ 3}  8Y^{ 3}. There are cubes and a minus sign so my immediate thought is, can I write it as a difference of cubes? I know that 8 is 2^{ 3} so I can write the expression as = X^{ 3}  2^{ 3}Y^{ 3} = X^{ 3}  (2Y)^{ 3} = (X  2Y)(X^{ 2}  X(2Y) + (2y)^{ 2}) = (X  2Y)(X^{ 2}  2XY + 4y^{ 2}) For problem 3, first take out a common factor of 8. Can you see how to express the 4th problem as a difference of cubes? Penny 

