Square of numbers close to multiples of power of 10

This is an adaptation of the previous post Square of numbers close to powers of 10

Lets take some examples 389 , 77 , 416

389 is near to 400.

Step 1:
Difference = 389-400=-11

Step 2:
Square of difference = 121 This is the right side ,but 1 is carried to the left side.
So now right hand side becomes 21 with carry 1.

Step 3:
Add 389 and  -11 = 378
Multiply this with 4(because 4*100= 400 ie. 4 times a power of 10)
378*4 = 1512
This is the left side.But now we need to add the carry from right side 1.
So 1512+1=1513

Answer 3892= 151321

316 is near to 300
Step1:
Difference =316-300=16

Step2:
Square of 16=256
So right side is 56 with carry 2.

Step 3:
316+16=332
332*3=996
Add the carry 2 to 996 = 998

Answer 3162= 99856

77 is near to 80
Step1:
Difference = 77-80=-3
Step2:Square of -3 = 9
Right side =9
Step3:
77-3=74
74*8=544
Left side =592

Answer 772= 5929




Square of numbers close to powers of 10

There is a shortcut to find square of numbers close to powers of 10 like 82 , 952 , 1132

Let's learn this by solving the examples
82
8 is close to the power of 10. ie 10.
Find the difference between 8 and 10.
8-10 = -2.

Find the square of that difference , here it is 4.
This is the right side of the answer.

Add the number(8) with the difference(-2)
=8+-2=6
This is the left side of the answer.

So answer is 64.

952
Step1:95-100=-5
Step2:Right side
          Square of -5 =25
Step 3:Left side
           Add 95 and -5= 90
Answer =9025

1132
Step1:113-100=-13
Step2:Right side
          Square of 13=169
          Now right side is only 69 and the one is carry.This 1 should be added to left  hand side answer.
Step 3:Left side
           Add 113 and 13 =126.
           Now add the carry from step 2 ,ie.1 to 126.
           ie.126+1=127
Answer =12769



Shortcut for multiplication when last digits added gives 10

Here we will discuss a shortcut to multiply when last digits added gives ten.

Eg. 42*48 , 56*54 , 63*67 , 114*116

The two conditions to use this are
1) tens place should be same .Eg. 42*48 can be calculated, but not 32*48.
2)Sum of last digits is 10. Eg. 42*48 . Last digits added= 2+8=10.

The answer has left and right portions.(Let's use the example 42*48)
1)Right portion =Product of last  one digit of each number= 2*8=16.
2)Left portion
  Let x = Number in the beginning(excluding last digit)-Here it is 4.
So left portion is x*(x+1)
Here 4*(4+1)=4*5=20

Answer = 2016

Let's solve the other examples.
56*54
Right = 6*4 =24
Left = 5*(5+1)=30
Answer=3024

63*67 = [6*7]|[3*7]
=4221

114*116
Right = 4*6=24
Left = 11*12=132
Answer=13224