## Mental Maths using Squares to help Multiply Tricks and Shortcuts

Two Numbers that Differ by 1
If a > b then a x b = a2 – a
Ex.: 35 x 34 = 1225 – 35 = 1190
If a < b then a x b = a2 + a
Ex.: 35 x 36 = 1225 + 35 = 1260

Two Numbers that Differ by 2
a x b = [(a + b)/2]2 -1
Ex.: 26 x 28 = 272 -1 = 729 – 1 = 728

Two Numbers that Differ by 3 (a < b)
a x b = (a + 1)2 + (a – 1)
Ex.: 26 x 29 = 272 + 25 = 729 + 25 = 754

Two Numbers that Differ by 4
a x b = [(a + b)/2]2 – 4
Ex.: 64 x 68 = 662 – 4 = 4356 - 4 = 4352

Two Numbers that Differ by 6
a x b = [(a + b)/2]2 – 9
Ex.: 51 x 57 = 542 – 9 = 2916 – 9 = 2907
Two Numbers that Differ by an Even Number: a < b and c = (b – a)/2
a x b = [(a + b)/2]2 – c2
Ex.: 59 x 67 = 632 – 42 = 3969 – 16 = 3953

Two Numbers that Differ by an Odd Number: a < b and c = [1 + (b – a)]/2
a x b = (a + c)2 – [b + (c –1)2
Ex.: 79 x 92 = 862 – (92 + 36) = 7396 – 128 = 7268

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