Difference of squares

Algebra Level 2

What is the difference between 222 2 { 222 }^{ 2 } and 197 2 { 197 }^{ 2 } ?

DO NOT USE A CALCULATOR!


The answer is 10475.

Thiago Baldissarelli by Thiago Baldissarelli , 31, Brazil

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3 solutions

a = 222 a n d b = 197 a 2 − b 2 = ( a + b ) ( a − b ) 222 2 − 197 2 = ( 222 + 197 ) ∗ ( 222 − 197 ) = 419 ∗ 25 = 10475 a=222\quad and\quad b=197\\ { a }^{ 2 }-{ b }^{ 2 }=(a+b)(a-b)\\ \\ { 222 }^{ 2 }-{ 197 }^{ 2 }=(222+197)*(222-197)=419*25=10475

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Vivek Rajak
Nov 7, 2014

a=square (200+22)

b=square(200-3)

a-b=[40000+484+8800]-[40000+9-1200]

a-b=40000+484+8800-40000-9+1200

a-b=10475

1 Helpful 0 Interesting 0 Brilliant 0 Confused

22 2 2 − 19 7 2 = ( 222 + 197 ) ( 222 − 197 ) = ( 419 ) ( 25 ) = 10475 222^2-197^2=(222+197)(222-197)=(419)(25)=\boxed{10475}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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