Question

Answer 1

`4x^3 - 16x = 4x (x^2 - 4) = 4x(x-2)(x+2) `

`x^4 - y^4 = (x^2)^2 - (y^2)^2 = (x^2 - y^2)(x^2 +y^2) = (x-y)(x+y)(x^2 + y^2)`

`3x^2 y - 6xy^2 +3y^3 = 3y(x^2 - 2xy + y^2) = 3y(x - y)^2`

`x^2 + y^2 - 4 + 2xy = (x^2 + 2xy + y^2) - 4 = (x+y)^2 -4 = (x+y-2)(x+y+2)`

`x^2 + 2x -y^2 +1 = (x^2 + 2x + 1) - y^2 = (x+1)^2 - y^2 = (x+1+y)(x+1-y) `

 

Answer 2

`a^2 - b^2 -12a + 12b = (a^2 - b^2) - (12a - 12b) = (a-b)(a+b)- 12(a-b) = (a-b)(a+b-12) `

`xy^2 + x^2 y + 1/4 y^3  = y (x^2 + xy + 1/4 y^2) = y(x + 1/2y)^2`

`x^2 - 25y^2 - 6x + 9 = (x^2 - 6x + 9) - (5y)^2 = (x - 3)^2 - (5y)^2 = (x - 3+5y)(x-3=5y) `

`4x^2 - 25y^2 +4x + 1 = (4x^2 + 4x + 1) - 25y^2 = (2x + 1)^2 - (5y)^2 = (2x+1+5y)(2x+1-5y)`