## Mental Maths Multiplication and Squaring Tricks and Shortcuts

Some useful formulae
Formula: (a+b)2 = a2 + 2ab + b2
Ex.: 492 = (40 + 9) 2 = 1600 + 720 + 81 = 2401

Formula: (a-b) 2 = a2 –2ab + b2
Ex.: 56 = (60 – 4) 2 = 3600 – 480 + 16 = 3136

Formula: (a+b) (a-b) = a2 – b2
Ex.: 64 x 56 = (60 – 4) (60 + 4) = 3600 – 16 = 3584

Formula: (a+b) (c+d) = (ac + ad) + (bc + bd)
Ex.: 23 x 34 = (20 + 3) (30 + 4) = 600 + 80 + 90 + 12 = 782

Formula:(a+b) (c-d) = (ac – ad) + (bc – bd)
Ex.: 34 x 78 = (30 + 4) (80 – 2) = 2400 –60 + 320 – 8 = 2652

Formula:(a-b) (c-d) = (ac – ad) – (bc – bd)
Ex.: 67 x 86 = (70 – 3) (90 – 4) = 6300 – 280 – 270 + 12 = 5762

X = 1 to 9 & Y = Any Number
Technique: (X5) 2 = 100X(X+1) + 25
Ex.: 652 = 600(7) + 25 = 4200 + 25 = 4225

Technique: 25 x Y = (Y x 100)/4
Ex.: 25 x 76 = 7600/4 = 1900

Technique: 50 x Y = (Y x 100)/2
Ex.: 50 x 67 = 6700/2 = 3350

Technique: 75 x Y = 3(Y x 100)/4
Ex.: 75 x 58 = (5800 x 3)/4 = 17400/4 = 4350

Tricks using (X5) 2
Technique: (X5 – a) 2 = (X5) 2 – X5(2a) + a2
Ex.: 632 = (65 – 2) 2 = 4225 – 260 + 4) = 3969

Technique: (X5 + a) 2 = (X5) 2 + X5(2a) + a2
Ex.: 672 = (65 + 2) 2 = 4225 + 260 + 4) = 4489

Squaring Numbers 52 to 99
Technique: a2 = [a - (100 – a)]100 + (100 – a) 2
Ex.: 932 = (93 – 7)100 + 72 = 8649

Squaring Numbers 101 to 148
Technique: a2 = [a + (a – 100)]100 + (a – 100) 2
Ex.: 1082 = (108 + 8)100 + 82 = 11664

Squaring Numbers near 1000
Technique: a2 = [a – (1000 – a)]1000 + (1000 – a) 2
Ex.: 9942 = (994 – 6)1000 + 6 2 = 988036

Technique: a2 = [a + (a – 1000)]1000 + (a – 1000) 2
Ex.: 10072 = (1007 + 7)1000 + 72 = 1014049

Squaring Numbers that end in 1
Technique: a2 = (a – 1) 2 + 2a - 1
Ex.: 61 2 = 60 2 + 122 - 1 = 3600 + 121 = 3721

Squaring Numbers that end in 4
Technique: a2 = (a + 1)2 – (2a + 1)
Ex.: 442 = 452 – (88 + 1) = 2025 - 89 = 1936

Squaring Numbers that end in 6
Technique: a2 = (a - 1)2 + (2a - 1)
Ex.: 562 = 552 + 112 - 1 = 3025 + 111 = 3136

Squaring Numbers that end in 9
Technique: a2 = (a + 1) 2 – (2a + 1)
Ex.: 792 = 802 – (158 + 1) = 6400 – 159 = 6341

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