Answer:
The product of (a+b)(a-b) is [tex]a^2 - b^2[/tex]
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
[tex]a^2 -ab+ab - b^2[/tex]
combine like terms
[tex]a^2 - b^2[/tex]
The product of (a+b)(a-b) is [tex]a^2 - b^2[/tex]
Shortcut is we apply an identity
[tex]a^2 - b^2 = (a+b)(a-b)[/tex]
(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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