SOLUTION: Compute
1234567890^2 - 2 \cdot 1234567890 \cdot 1234567890 + 1234567891^2
without using a calculator.
Algebra.Com
Question 1209116: Compute
1234567890^2 - 2 \cdot 1234567890 \cdot 1234567890 + 1234567891^2
without using a calculator.
Answer by math_tutor2020(3817) (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.
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