1)
a) x^2 + 4xy - 36 + 4y^2
= (x + 2y)^2 - 36
= (x + 2y + 6)(x + 2y - 6)
b) = 4x(x - 1)
c) = (a + b)^2 - 9
= (a + b - 3)(a + b + 3)
d) (x - y)^2 - (3z)^2
= (x - y - 3z)(x - y + 3z)
e) = x(4x^2 - 12x + 9)
= x [(2x)^2 - 12x + 3^2]
= x(2x - 3)^2
g) x^2 - xy + 2020x - 2020y
= x(x - y) + 2020(x - y)
= (x + 2020)(x - y)
h) x^2 + 7x + 12
= x^2 + 4x + 3x + 12
= (x + 3)(x + 4)
i) x^2 - 5x + 6
= x^2 - 2x - 3x + 6
= x(x - 2)( - 3(x - 2)
= (x - 3)(x - 2)
k) = (x - y)(x + y) - 4(x - y)
= (x + y - 4)(x + y)
q) = 3x(x - y) - (x - y)
= (3x - 1)(x - y)
s) 7x(y - 4)^2 - (4 - y)^3
= 7x(4 - y)^2 - (4 - y)^3
= (7x - 4 + y)(4 - x)^2
t) x^4 + 2x^3 - 4x - 4
= x^4 + 2x^3 + x^2 - x^2 - 4x - 4
= x^2(x + 1)^2 - (x + 2)^2
= (x^2 + x)^2 - (x + 2)^2
= (x^2 + 2x + 2)(x^2 - 2)
= (x^2 + 2x + 2)(x - √2)(x + √2)
w) x^3 - x^2 - 5x + 125
= (x^3 + 125) - x(x + 5)
= (x + 5)(x^2 - 5x + 25) - x(x + 5)
= (x + 5)(x^2 - 6x + 25)