SOLUTION: one of the factors of the expression (2a+5b)^3+(2a-5b)^3 would be? a)4a b)10b c)2a+5b d)2a-5b also give me the solution!thankyou!!

Question 714736: one of the factors of the expression (2a+5b)^3+(2a-5b)^3 would be?
a)4a b)10b
c)2a+5b d)2a-5b
also give me the solution!thankyou!!
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

As weird as this may look this expression, in essence, is a sum of cubes. And we have a factoring pattern for a sum of cubes:

So we can use this pattern (with the "p" being "2a+5b" and the "q" being "2a=5b") to factor :

Now we simplify the factors. In the first factor the 5b's cancel out leaving 2a+2a or 4a. So the multiple-choice answer is A.

To simplify more easily we can use the following patterns:

Using these patterns we get:

Simplifying...

The 20ab's cancel out. And two of the 's cancel out. Adding the other like terms we get:

Altogether

factors into:

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