Questions on Algebra: Distributive, associative, commutative properties, FOIL answered by real tutors!

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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
: (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!
Answer by jim_thompson5910(9401) About Me  (Show Source):
You can put this solution on YOUR website!

(2z+5)(4z^2-10z+25) Start with the given expression.


2z(4z^2-10z+25)+5(4z^2-10z+25) Expand.


(2z)*(4z^2)+(2z)*(-10z)+(2z)*(25)+(5)*(4z^2)+(5)*(-10z)+(5)*(25) Distribute.


8*z^3-20*z^2+50*z+20*z^2-50*z+125 Multiply.


8*z^3+125 Now combine like terms.


Notice how 8*z^3+125 is a binomial where both terms are cubes of other terms. In other words, 8*z^3=(2z)^3 and 125=(5)^3. The short cut you mentioned would use the sum of cubes formula A^3+B^3=(A+B)(A^2-AB+B^2) to expand the original problem (which is a much faster way to solve the problem).


So (2z+5)(4z^2-10z+25) expands to 8*z^3+125.



In other words, (2z+5)(4z^2-10z+25)=8*z^3+125.