SOLUTION: (2z+5)(4z-10z+25) The 4z is supposed to be squared but I can't figure out how to type that on here. The portion of the chapter where this problem is found is called Creati

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: (2z+5)(4z-10z+25) The 4z is supposed to be squared but I can't figure out how to type that on here. The portion of the chapter where this problem is found is called Creati      Log On


   

Question 147759This question is from textbook
: (2z+5)(4z-10z+25)
The 4z is supposed to be squared but I can't figure out how to type that on here.
The portion of the chapter where this problem is found is called Creating the Sum and Difference of Cubes. It gives you a short cut for finding the solution, but does not give any detail to help me figure out how they reached the answer. I can not except the solution they want me to give without knowing what is done to reach that answer. They give the solution in the end of the chapter and I understand why the first and last terms are what they are, but can not figure out why the middle term disappears. Please help! This question is from textbook

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%282z%2B5%29%284z%5E2-10z%2B25%29 Start with the given expression.


2z%284z%5E2-10z%2B25%29%2B5%284z%5E2-10z%2B25%29 Expand.


Distribute.


8%2Az%5E3-20%2Az%5E2%2B50%2Az%2B20%2Az%5E2-50%2Az%2B125 Multiply.


8%2Az%5E3%2B125 Now combine like terms.


Notice how 8%2Az%5E3%2B125 is a binomial where both terms are cubes of other terms. In other words, 8%2Az%5E3=%282z%29%5E3 and 125=%285%29%5E3. The short cut you mentioned would use the sum of cubes formula A%5E3%2BB%5E3=%28A%2BB%29%28A%5E2-AB%2BB%5E2%29 to expand the original problem (which is a much faster way to solve the problem).


So %282z%2B5%29%284z%5E2-10z%2B25%29 expands to 8%2Az%5E3%2B125.



In other words, %282z%2B5%29%284z%5E2-10z%2B25%29=8%2Az%5E3%2B125.