Post the entire exampleword problem you have been assigned f

Post the entire example/word problem you have been assigned from the textbook. Then fully explain how you would go about finding the solution. Please explain all steps in a way that a struggling classmate could understand and learn from your methods.

(Polynomial Functions and Factoring)

Question. Explain in detail how to find the product of the sum and difference of two terms. Give a example with your explaination

Solution

let two terms be a and b

sum of two terms = a+b

difference of two terms = a-b

product = (a+b)(a-b)

distributing a+b over a-b

(a+b)(a-b) = a^2 - ab + ab - b^2 = a^2 - b^2

therefore, product of sum and difference of two terms = difference of squares of the terms

example : 4x^2 - 9

4x^2 can be written as (2x)^2

and 9 = 3^2

therefore, applying the formula

4x^2 - 9 = (2x)^2 - 3^2 = (2x+3) (2x-3 )