Mental Maths Multiplication and Squaring Tricks

Hi, welcome to nrrbeassistance.blogspot.com. Mental Maths Multiplication and Squaring Tricks and Shortcuts for the jobs, bank exams like RBI / SBI / IBPS CWE / RRB. Useful in the preparation of quantitative aptitude &/ numerical ability for the pupil preparing probationary officers (PO) / specialist officer (SO) / manager / assistants / clerks posts and others.

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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