# CLASS-8PRODUCT OF SUM & DIFFERENCE OF TWO TERMS

Product of Sum and Difference of Two Terms –

Let us take two terms ‘x’ & ‘y’ and find the product of their sum (x+y) and difference (x-y).

There are some laws which has been proved with logical calculation –

A)  (x+y) (x-y) =  x(x-y) + y(x-y)

=  x² - xy + yx - y²

=  x² - y²

Or,     x²- y² = (x+y) (x-y)

In other words, the product of the sum and the difference of two terms are equal to the difference of their squares.

This can also be expressed such as –

(first term + second term) X (first term – second term) = (first term)² - (second term)²

There are some example are given below for your better understanding –

Example.1)   (m+5)(m-5)

= m(m-5) + 5(m-5)

=  m² -5m + 5m – 25

=  m² - 5²

Example.2)  (2x+3y)(2x-3y)

=  2x(2x-3y) + 3y(2x-3y)

=  (2x)²- 6xy + 6xy – (3y)²

=  (2x)²- (3y)²

Example.3)  (3x-5y)(3x+5y)

=  3x(3x+5y) – 5y(3x+5y)

=  (3x)²+ 15xy – 15xy – (5y)²

=  (3x)²- (5y)²

Example.4)  (2aᶟ+3b²) (2aᶟ- 3b²)

=  2aᶟ(2aᶟ- 3b²) + 3b²(2aᶟ- 3b²)

=  (2aᶟ)²- 6aᶟb²+ 6aᶟb²- (3b²)²

=  (2aᶟ)²- (3b²)²

5a            3a           5a            3a

Example.5)  ( -------- - --------) ( -------- + --------- )

6b            5b           6b            5b

5a         5a          3a            3a           5a          3a

= ------- ( ------- + ------- ) - -------- ( ------- + ------- )

6b         6b          5b            5b           6b          5b

5a           15a²         15a²          3a

= (-------)² + -------- - -------- - (--------)²

6b            30b²         30b²          5b

5a                3a

=  (--------)² -  (--------)²

6b                5b