Question

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

Answer 1

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)

`(4x^(2)-y^(2))/(8x^(2)+10xy+3y^(2))*(4x^(2)-9xy-9y^(2))/(2x^(2)-5xy-3y^(2))\\\\\\=((2x+y)*(2x-y))/((2x+y)(4x+3y))*(((x-3y)(4x+3y))/((x-3y)(2x+y))\\\\\\=(2x-y)/(2x+y)`