Mental Math Trick

Algebra Level 2

You can change a regular multiplication problem into a binomial multiplication problem to do mental math faster:

49 × 47 ( 50 − 1 ) × ( 50 − 3 ) 2500 − 50 − 150 + 3 2503 − 200 2303 49 \times 47 \\ (50-1) \times (50-3) \\ 2500 - 50 - 150 + 3 \\ 2503 - 200 \\ 2303

Try it yourself: what's 92 × 98 ? 92 \times 98 ? (No paper or calculators allowed!)


The answer is 9016.

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Jason Dyer by Jason Dyer

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2 solutions

Jason Dyer Staff
Oct 6, 2016

92 × 98 ( 100 − 8 ) × ( 100 − 2 ) 10000 − 200 − 800 + 16 10016 − 1000 9016 92 \times 98 \\ (100-8) \times (100-2) \\ 10000 - 200 - 800 + 16 \\ 10016 - 1000 \\ 9016

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Let's try another way

92x98 = (95-3)*(95+3) = 95^2 - 3^2 = 9025 - 9 =9016

95^2 = 100*9(9+1) +25 = 9025

Prove = (10a +5)^2 = 100a^2 + 100a + 25 = 100a(a+1) + 25

3 Helpful 0 Interesting 0 Brilliant 0 Confused

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