# Arithmetical Calculations: How to Multiply

## Multiplication of different items: (A+B)(X+Y)=A(X+Y)+B(X+Y) Square of an addition of two items: (A+B)2=A2+2AB+B2 Square of a difference between two items: (A-B)2=A2-2AB+B2 Multiply addition and difference of two factors: (A+B)(A-B)2=A2-B2.

Arithmetical calculations: How to multiply

Rakhi Sharma Devendra Kumar* and Awadhesh Kishore*

Institute for Development of Technology for Rural Advancement, Mathura-281004 (INDIA)

*Sarvoday Mahavidyalaya, Chaumuhan-281406, Mathura (INDIA)

Summary:

Multiplication of different items: (A+B)(X+Y)=A(X+Y)+B(X+Y).

Square of an addition of two items: (A+B)2=A2+2AB+B2.

Square of a difference between two items: (A-B)2=A2-2AB+B2.

Multiply addition and difference of two factors: (A+B)(A-B)2=A2-B2.

Keywords:

Addition, Arithmetic, Calculations, Difference, Different items, How to, Multiply.

Multiplication in Arithmatic is so easy if we follow a fixed procedure. If we have to multiply two Arithmetical items having two factors in each. We can use simple equations as illustrated below:

Multiplication of different items:

(A + B) (X + Y) = A(X + Y) + B(X + Y)

Or say:

(A + B) (X + Y) = AX + AY + BX + BY (Formula… 1)

Example:

(3x+8)( 4x-7)

=3x (4x – 7) + 8(4x – 7)

3x* 4x – 3x*7 + 8* 4x – 8*7

=12×2 – 21x + 32x  - 56

12×2  + 11x – 56 (ANSWER)

Square of an addition of two items:

When we have to square a addition, we need to add twice of their multiplication in sum of squares of both the items.

(A + B)2= (A + B)(A + B) = A(A + B) + B(A + B)

=A2 + AB + AB + B2

Or say:

(A + B)(A + B)=A2 + 2AB + B2 (Formula… 2)

Example:

(3x+8)2

= (3x)2 + 2 (3x) (8) + (8)2

= 9×2 + 48x + 64 (ANSWER)

Square of a difference between two items:

When we have to square a difference, we need to subtract twice of their multiplication from sum of squares of both the items.

(A – B)2 = (A – B)(A – B)=A(A – B) – B(A – B)

=A2 – AB – AB + B2

Or say:

(A – B)2= (A – B) (A – B)=A2 – 2AB + B2 (Formula… 3)

Example:

(4x-7)2

=(4x)2 – 2(4x)(7) + (7)2

=16×2 – 56x + 49  (ANSWER)

Multiply addition and difference of two factors:

When we need to multiply addition and difference of two factors, we need to subtract square of second factor from the square of first factor.

(A + B) (A – B) = A (A – B) + B(A – B)

=A2 – AB + AB – B2

Or say:

(A + B) (A – B) = A2 – B2 (Formula… 4)

Example:

(3x-4y) (3x+4y)

=(3x)2 – (4y)2