Q:

Choose the correct product of (7x − 3)(7x + 3). 49x2 + 9 49x2 − 42x + 9 49x2 − 9 49x2 + 42x + 9

Accepted Solution

A:
The product of factors is [tex]49x^2 - 9[/tex]. Option C shows the correct expression of the product.What is a product?A product is the result of multiplication or an expression that identifies factors to be multiplied.Given factors are (7x − 3) (7x + 3).We need to find out the product of the given factors.Product = [tex](7x - 3)\times (7x + 3)[/tex]Product = [tex]7x (7x +3) - 3 (7x + 3)[/tex]Product = [tex]49 x^2 + 21 x - ( 21 x + 9)[/tex]Product = [tex]49x^2 + 21x - 21 x - 9[/tex]Product = [tex]49x^2 - 9[/tex]The given factors are a difference of squares, where[tex]a^2 - b^2 = (a + b)(a - b)[/tex]We can directly simplify the factors by using the above formula where a = 7x and b = 3.[tex](7x -3)(7x + 3) = (7x)^2 - (3)^2[/tex][tex](7x -3)(7x + 3) = 49 x^2 - 9[/tex]Hence we can conclude that the product of factors is [tex]49x^2 - 9[/tex]. Option C shows the correct expression of the product.To know more about the product, follow the link given below..