# Multiplication Shortcut Part 2

**Squaring Certain Numbers**

Let N stands for a number to be squared.

**If the number ends in 1 or 6:**

(N – 1) × (N – 1) + (N + N – 1)

Example: 91^2 = (91 – 1) × (91 – 1) + (91 + 91 – 1) = 90 × 90 + 91 + 90 = 8100 + 91 + 90 = 8281

**If the number ends in 5 (two-digit number):
**First digit × (First digit + 1); attach 25

Example: 45^2= 4 × (4+1); attach 25 = 2025

**If the number ends in 5 (three-digit number):
**First two digit × (First two digit + 1); attach 25

Example: 455^2= 45 × (45+1); attach 25 = 207025

**If the number ends in 4 or 9:
**(N + 1) × (N + 1) – (N + N – 1)

Example: 34^2 = (34 + 1) × (34 + 1) – (35 + 35 – 1) = 35 × 35 + 69

= [3 × (3+1); attach 25] – 69 = 1225 – 69= 1156

**Multiplication of numbers having small differences**

**Difference of 1:**

Square the larger number, then subtract the larger number

Example: Multiply 14 × 13:

14 × 14 = 196; 196 – 14 = 182

Or Square the smaller number, then add the smaller number

Example: multiply 14 × 13;

13 × 13 = 169; 169 + 13 = 182

**Difference of 2:**

Square the average of two number (middle number or in-between) and then subtract 1

Example: Multiply 31 × 29;

30 × 30 = 900; 900 – 1 = 899

**Difference of 3:
**Example: Multiply 37 × 34:

Step a. Add 1 to the smaller number then square the sum

34 + 1= 35; 35^2 = 1225

Step b. Subtract 1 from the smaller number then add it with the step a.

34 – 1= 33; 1225 + 33 = 1258

**Difference of 4:
**Square the average of two numbers and subtract 4

Example: Multiply 57 × 53:

Here, Average: 55 [(smaller number + 2) or (larger number – 2)] 55 × 55 = 3025; 3025 – 4 = 3021

**Difference of 6:
**Square the average of two numbers and subtract 9

Example: Multiply 57 × 51:

Here, Average: 54 [(smaller number + 3) or (larger number – 3)] 54 × 54 = 3025; 2916 – 9 = 2907

**Multiplication of numbers between 91 to 99**

Step 1: Find difference from 100 for each numbers.

Step 2: Add each difference, then subtract the result from 100. The final result will be first two digit of the required multiplication.

Step 3: Multiply each difference from step 1. The result will be last two digit of the required multiplication. If you get one digit number in this step, you need to place a zero before the digit.

**Multiply a number by 11**

Multiplication of any two digit number with 11 can be done by two simple steps. First write the two digit separately. Second place the sum of those digit in-between.

**Multiply a number by 21, 31, 41, 51, etc**

Multiply the number by the first digit of the multiplier (21, 31, 41, 51, etc), multiply the result by 10, and add the number.

Example: Multiply 57 × 51:

57 × 5 = 285;

285 × 10 = 2850;

2850 + 57 = 2907

Multiply 87 × 21: 87 × 2 = 174; 174 × 10 = 1740; 1740 + 87 = 1827