Answer:
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)
[tex]\frac{4x^{2}-y^{2}}{8x^{2}+10xy+3y^{2}}*\frac{4x^{2}-9xy-9y^{2}}{2x^{2}-5xy-3y^{2}}\\\\\\=\frac{(2x+y)*(2x-y)}{(2x+y)(4x+3y)}*\frac{((x-3y)(4x+3y)}{(x-3y)(2x+y)}\\\\\\=\frac{2x-y}{2x+y}[/tex]
