Differences of squares

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What is 50 0 2 − 49 9 2 500^2 - 499^2 ?

Please don't use your calculator to solve this

Details and Assumptions : Look at this note to give you an easier way to solve it without using a calculator


The answer is 999.

Daniel Lim by Daniel Lim , 21, Singapore

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7 solutions

敬全 钟
Jan 10, 2014

Haha. This is very easy. The given expression can be factorized as

50 0 2 − 49 9 2 = ( 500 − 499 ) ( 500 + 499 ) 500^2-499^2 = (500-499)(500+499)

50 0 2 − 49 9 2 = 999 500^2 - 499^2 = \boxed{999}

Tada! \text{Tada!}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

When you are required to solve differences of perfect squares, try this identity:

a 2 − b 2 = ( a − b ) ( a + b ) a^2-b^2=(a-b)(a+b)

Example:

29 × 31 = ( 30 − 1 ) ( 30 + 1 ) = 3 0 2 − 1 2 = 900 − 1 = 899 29\times31=(30-1)(30+1)=30^2-1^2=900-1=899

敬全 钟 - 7 years, 5 months ago

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wow

Daniel Lim - 7 years, 5 months ago

wow can you ask aaron saw to give me the book u mentioned?

Daniel Lim - 7 years, 5 months ago
Daniel Lim
Jan 10, 2014

Based on the post I shared, 50 0 2 = 49 9 2 + 500 + 499 500^2 = 499^2 + 500 + 499

If we subtract 49 9 2 499^2 from both sides,

50 0 2 − 49 9 2 = 500 + 499 500^2 - 499^2 = 500 + 499

= 999 =\boxed{999}

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Shravan Kumar
Aug 23, 2015

The difference of squares is equal to the sum of the numbers. So 500^2-499^2=500+499=999

0 Helpful 0 Interesting 0 Brilliant 0 Confused

let 500=a 499=b

a^2-b^2=(a+b)(a-b)

=(999)(1)

=999

0 Helpful 0 Interesting 0 Brilliant 0 Confused

My solution is :

50 0 2 − 49 9 2 = ( 499 + 1 ) 2 − 49 9 2 500^{2}-499^{2}=(499+1)^{2}-499^{2}

49 9 2 + 499 + 499 + 1 − 49 9 2 499^{2}+499+499+1-499^{2}

so, we can subtract 49 9 2 499^{2}

and then 499 + 499 + 1 = 999 499+499+1=\boxed{999}

well, maybe it's too long, haha

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Use the identity: a 2 − b 2 = ( a + b ) ( a − b ) a^2-b^2=(a+b)(a-b) Substitute the values in the formula and solve: 50 0 2 − 49 9 2 = ( 500 + 499 ) ( 500 − 499 ) = 999 × 1 = 999 500^2-499^2=(500+499)(500-499)=999\times1=\boxed{999}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

50 0 2 − 49 9 2 500^{2}-499^{2}

= ( 500 − 499 ) ( 500 + 499 ) =(500-499)(500+499)

= 1 × 999 =1 \times 999

999 \boxed{999}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

l e t 500 b e x s o , x 2 − ( x − 1 ) 2 = 2 x − 1 = 2 ( 500 ) − 1 = 999 let 500 be x so, x^{ 2 }-(x-1)^{ 2 } = 2x-1 =2(500) - 1 =\boxed{999}

Shubham Gaikwad - 6 years, 11 months ago

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