Multiplication Tricks (3)

Algebra Level 1

Find the value of

97 × 97 \large 97 \times 97

Try without the use of a calculator

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The answer is 9409.

Angela Fajardo by Angela Fajardo , 19, Philippines

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3 solutions

Zee Ell
Nov 2, 2016

9 7 2 = ( 100 − 3 ) 2 = 10 0 2 − 2 × 3 × 100 + 3 2 = 10000 − 600 + 9 = 9409 97^2 = (100 - 3)^2 = 100^2 - 2×3×100 + 3^2 = 10000 - 600 + 9 = \boxed {9409}

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Viki Zeta
Nov 2, 2016

97 × 97 = 9 7 2 = ( 90 + 7 ) 2 = 9 0 2 + 2 ( 90 ) ( 7 ) + 7 2 = 8100 + 1260 + 49 = 9409 97 \times 97 = 97^2 = (90+7)^2 = 90^2 + 2(90)(7) + 7^2 = 8100 + 1260 + 49 = 9409

2 Helpful 0 Interesting 0 Brilliant 0 Confused

97 is 3 less than 100, we would subtract 3 from 97, 97-3=94(first part)

Also 3 2 = 09 3^2=0 9 (second part)

So 9 7 2 = 9409 97^2 =9409 (by taking first and second part together)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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