SOLUTION: (5x-1)^2 I know the answer is 25x^2-10x+1 But when I try to solve I only come up with 25x^2+1 I don't understand where the -10x comes from, I appreciate any help, than

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: (5x-1)^2 I know the answer is 25x^2-10x+1 But when I try to solve I only come up with 25x^2+1 I don't understand where the -10x comes from, I appreciate any help, than      Log On


   

Question 541506: (5x-1)^2
I know the answer is 25x^2-10x+1
But when I try to solve I only come up with 25x^2+1
I don't understand where the -10x comes from,
I appreciate any help,
thank you!!
Found 3 solutions by Earlsdon, friesr, josmiceli:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Use the FOIL method to multiply the binomials:
%285x-1%29%285x-1%29+=+25x%5E2-5x-5x%2B1 Simplify to:
25x%5E2-10x%2B1

Answer by friesr(113) About Me  (Show Source):
You can put this solution on YOUR website!
The perfect square factoring formula is:
%28a+%2B+b%29%5E2+=+a%5E2+%2B+2ab+%2B+b%5E2%0D%0A
---
Your problem:
%285x-1%29
---
%285%5E2%29+%28x%5E2%29+%2B+2%285%29%28-1%29%28x%29+%2B+%28-1%29%5E2
---
Your answer:
25x%5E2+-+10x+%2B+1
===

You may want to note these formulas for the future:
1. a%5E2+-+b%5E2+=+%28a-b%29%28a%2Bb%29 Difference of squares
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2. a%5E2+%2B+2ab+%2B+b%5E2+=+%28a%2Bb%29%5E2 Perfect square
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3. a%5E2+-+2ab+%2B+b%5E2+=+%28a-b%29%5E2 Perfect square
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4. a%5E3+-+b%5E3+=+%28a-b%29%28a%5E2+%2B+ab+%2B+b%5E2%29 Difference of cubes
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5. a%5E3+%2B+b%5E3+=+%28a%2Bb%29%28a%5E2+-+ab+%2B+b%5E2%29 Sum of cubes

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Here is a general case of the squaring:
+%28a+-+b%292+=+%28a+-+b%29%2A%28a+-+b%29+
+%28a+-+b%29%2A%28a+-+b%29+=+a%5E2+-+a%2Ab+-+a%2Ab+%2B+b%5E2+
--------------
Now your problem:
+%285x+-+1%29%5E2+=+%285x+-+1%29%2A%285x+-+1%29+
+%285x+-+1%29%2A%285x+-+1%29+=+25x%5E2+-+5x+-+5x+%2B+1+
+%285x+-+1%29%2A%285x+-+1%29+=+25x%5E2+-+10x+%2B+1+
In the FOIL method, the +-5x+ terms come
from the Outer and Inner multiplications.