24 Factor completely 5x2y 45xye 40y 25 Factor completely 2xg

24. Factor completely: 5x2y 45xye 40y 25. Factor completely: -2xgy 16x2y 32xy 26. Factor completely: 3x4 21xsy 54x2ye

Solution

24. 5x²y + 45xy²+40y³

     5y(x²+9xy +8y²)   =   5y(x²+ 8xy + xy + y²)

                                   = 5y(x(x+8y)+y(x+y))   = 5y(x+y)(x+8y)

25. -2x³y² + 16x²y³ -32xy⁴

      -2xy²(x² -8xy +16y²)   =   -2xy²(x²-4xy-4xy +16y²)

                                           = -2xy²(x(x-4y) -4y(x-4y))

                                           = -2xy²(x-4y)(x-4y) =   -2xy²(x-4y)²

^26.    3x⁴ -21x³y -54x²y² =   3x²(x²-7xy -18y²)

                                         = 3x²(x² -9xy + 2xy -18y²)

                                         = 3x²(x(x-9y) +2y(x-9y))

                                         = 3x²(x+2y)(x-9y)