1) 4x2 – 25 + (2x + 7)(5 – 2x)
= 4x2 – 25 + 10x – 4x2 + 35 – 14x
= -4x + 10

2) 3(x+ 4) – x2 – 4x
= 3x + 12 – x2 – 4x
= -x2 – x + 12

3) 5x2 – 5y2 – 10x + 10y
= 5(x2 – y2) – 10(x – y)
= 5(x + y)(x – y) – 10(x – y)
= (x + y)(5x – 5y – 10)

4) x2 – xy + x – y
= x(x – y) + 1(x – y)
= (x + 1)(x – y)

5) ax – bx – a2 + 2ab – b2
= (a – b)(x – a + 2b)

6) x2 + 4x – y2 + 4
= (x + 2)(x + 2) – (y + 2)(y – 2)
= (x + 2)2 – (y + 2)(y – 2)

7) x3 – x2 – x + 1
= (x – 1)(x2 – 1)
= (x – 1)(x + 1)(x – 1)
= (x – 1)2(x + 1)

8) x4 + 6x2y + 9y2 - 1
= (x2 + 3y)2 - 1

9) x3 + x2y – 4x – 4y
= x(x2 + xy – 4) – 4(x + y)
= x(x2 + xy – 4) – 4(x + y)

10) x3 – 3x2 + 1 – 3x
= (x – 1)(x2 – 3x – 1)

11) 3x2 – 6xy + 3y2 – 12z2
= 3(x – y)2 – 12z2

12) x2 – 2x – 15
= (x – 5)(x + 3)

13) 2x2 + 3x – 5
= (2x – 1)(x + 5)

14) 2x2 – 18
= 2(x2 – 9)
= 2(x – 3)(x + 3)

15) x2 – 7xy + 10y2
= (x – 5y)(x – 2y)

16) x3 – 2x2 + x – xy2
= x(x2 – 2x + 1 – y2)
= x(x – 1)2 – xy2