F.2 MATH.Factorize

Factorize:

5. x² -xy-3x+3y
= x(x-y)+3(-x+y) (<------可miss)
= x(x-y)-3(x-y)
= (x-y)(x-3)

6. m² +mn-m-n
= m(m+n)-(m+n)
= (m+n)(m-1)

17. a³ +a² b-a² c-abc
= a² (a+b)+ac(-a-b) (<------可miss)
= a² (a+b)-ac(a+b)
= (a+b)(a² -ac)

18. a³ -3a² +2ax-6x³
= a² (a-3)+2x(a-3x² )

19. -ax-bx-cx+ay+by+cy
= x(-a-b-c)+y(a+b+c) (<------可miss)
= -x(a+b+c)+y(a+b+c)
= (a+b+c)(y-x)

22. 2a² bc-4ab² c+12abc²
= 2abc(a-2b+6c)

23. r(p-q)-s(p-q)
= (p-q)(r-s)

29. a(x+y)² -ab(x+y)²
= (x+y)² (a-ab)

44. (3x+2y)² -(3x+2y)(x-y)
= (3x+2y)² (x-y) <-----((3x+2y)(3x+2y)(x-y))

(44.原理...a² -ab=a(a-b))

只係以我嘅諗法黎解答,但都希望幫到您

Ans:
5. x2次-xy-3x+3y
=x(x-y)-3(x-y)
=(x-y)(x-3)
6. m2次+mn-m-n
=m(m-1)+n(m-1)
=(m-1)(m+n)
17. a3次+a2次b-a2次c-abc
=a2次(a+b)-ac(a+b)
=a(a+b)(a-c)
18.a3次-3a2次+2ax-6x3次
=a2次(a-3)+2x(a-x2次)
19.-ax-bx-cx+ay+by+cy
=-x(a+b+c)+y(a+b+c)
=(a+b+c)(-x+y)
22.2a2次bc-4ab2次c+12abc2次
=2abc(a-2b+6c)
23.r(p-q)-s(p-q)
=(p-q)(r-s)
29. a(x+y)2次-ab(x+y)2次
=a(x+y)2次(1-b)
44.(3x+2y)2次-(3x+2y)(x-y)
=(3x+2y)(3x+2y-x+y)
=(3x+2y)(2x+3y)