How Can We Apply This Fact?

Algebra Level 1

It is known that 201 6 2 = 4064256 2016^2=4064256 .
Using this information, find the value of 2020 × 2012 2020 \times 2012 without using a calculator.


The answer is 4064240.

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Alex Li by Alex Li , 21, USA

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3 solutions

Chew-Seong Cheong
Aug 11, 2016

Relevant wiki: Properties of difference of two squares

2020 × 2012 = ( 2016 + 4 ) ( 2016 − 4 ) = 201 6 2 − 4 2 = 4064256 − 16 It is given that 201 6 2 = 4064256 = 4064240 \begin{aligned} 2020 \times 2012 & = (2016+4)(2016-4) \\ & = 2016^2 - 4^2 \\ & = \color{#3D99F6}{4064256} - 16 & \small \color{#3D99F6}{\text{It is given that }2016^2 = 4064256} \\ & = \boxed{4064240} \end{aligned}

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Oh, my you were here in 2016 and still uses and posts solutions on Brilliant. Legend.

Anonymous1 Assassin - 3 weeks ago

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Yup. All in all 8316 solutions.

Chew-Seong Cheong - 3 weeks ago
Alex Li
Aug 10, 2016

Call 2016 n.

2020, then, is n+4, and 2012 is n-4, and we know n^2 is 4064256.

Using substitution, we find that ( n + 4 ) ( n − 4 ) = n 2 − 16 = 4064256 − 16 (n+4)(n-4) = n^2-16 = 4064256 - 16

So our answer is 4064240!

8 Helpful 0 Interesting 0 Brilliant 0 Confused

2020*2012 = (2016+4)(2016-4) = 2016^2 - 16 = 4064256 - 16 = 4064240

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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