Use foil to explain how to find the product of (a + b)(a − b). then describe a shortcut that you could use to get this product without using foil

The product of (a+b)(a-b)  is

Step-by-step explanation:

Use FOIL to explain how to find the product of (a + b)(a − b)

FOIL is

Multiply First terms : a*a = a^2

Multiply Outside terms : a* -b = -ab

Multiply Inner  terms : b * a= ab

Multiply last terms : b * -b = -b^2

now we combine all the terms

combine like terms

The product of (a+b)(a-b)  is

Shortcut is we apply an identity

(a - b)(a + b)   =  a² -  b²

FOIL is an acronym for First, Outside, Inside, and Last

This method allows to find the product in the order First, Outside, Inside, and Last.

For the product (a + b)(a - b, using the FOIL method:

First: a(a)  = a²

Outside: a(-b)  =  -ab

Inside: b(a)   =  ab

Last:  b(-b)  =   -b²

Adding all the terms together, the expression becomes:

a²  -  ab  +  ab  +  b²

After simplification, the expression becomes:

a²  -  b²

A shortcut for finding the product is the difference of two squares

Using the difference of two squares rule:

(a  - b)(a + b)   =  a²  -  b²

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