Question

The product of sum and difference of two binomial like (x+y) and (x-y) isof two squares. (FERFENCEID)

Answer 1

The product of sum and difference of two binomial like (x+y) and (x-y) is x² -  y²

The first number = x

The second number = y

The sum of the two numbers = x + y

The difference of the two numbers = x - y

The product of the sum and the difference = (x+y)(x -y)

Note that the product of the sum and the difference = (x + y)(x - y)

This can be expanded by distributivity as shown below:

(x + y)(x - y) = x² + xy - xy - y²

(x + y)(x - y)  =  x² -  y²

This is the difference of two squares.

Therefore, the product of sum and difference of two binomial like (x+y) and (x-y) is x² -  y²

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