SOLUTION: Compute 1234567890^2 - 2 \cdot 1234567890 \cdot 1234567890 + 1234567891^2 without using a calculator.

Algebra ->  Expressions-with-variables -> SOLUTION: Compute 1234567890^2 - 2 \cdot 1234567890 \cdot 1234567890 + 1234567891^2 without using a calculator.      Log On


   

Question 1209116: Compute
1234567890^2 - 2 \cdot 1234567890 \cdot 1234567890 + 1234567891^2
without using a calculator.
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

1234567890 shows up repeatedly and 1234567891 is very close to the previous value.
Let's assign a variable to them.

x = 1234567890
x+1 = 1234567890+1
x+1 = 1234567891

The original expression condenses to
x^2 - 2x*x + (x+1)^2

Expand things out and simplify as much as possible.
x^2 - 2x*x + (x+1)^2
x^2 - 2x^2 + x^2+2x+1
2x+1

x^2 - 2x*x + (x+1)^2 fully simplifies to 2x+1.

Your original task of computing
1234567890^2 - 2*1234567890*1234567890 + 1234567891^2
is equivalent to computing
2*1234567890 + 1

I'll let the student take over from here.