Perform the indicated operation and simplify the result. 4x^2 - y^2
—————-
8x^2 + 10xy + 3y^2

Multiplied by

4x^2 - 9xy - 9y^2
———————
2x² -5x - 3y^2

Step-by-step explanation:

a² -b² = (a + b)(a - b)

4x² - y² = (2x)² - y² = (2x + y)(2x - y)

4x² - 9xy - 9y²

sum = -9xy

Product = 4x² *9y² = -36x² y²

Factors :  -12xy , 3xy

4x² - 9xy - 9y² =  4x² - 12xy + 3xy - 9y²

                       =   4x(x - 3y) + 3y(x - 3y)

                       = (x - 3y)(4x + 3y)

8x² + 10xy +3y²

sum = 10xy

Product = 8x² *3y² = 24x² y²

Factors :  4xy , 6xy

8x²  + 10xy + 3y²  = 8x²  + 4xy + 6xy + 3y²

                             =4x(2x + y) +3y(2x + y)

                            = (2x + y)(4x + 3y)

2x²  - 5xy  - 3y²  

sum = -5xy

Product = 2x² * -3y² = -6x² y²

Factors :  xy , -6xy

2x² - 5xy - 3y² = 2x² + xy -6xy - 3y²

                       = x(2x + y)-3y(2x + y)

                      = (x - 3y) (2x + y)

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

hope it