Maths 的問題 fast!!!!

1,
ab + ac - ad
= a(b) + a(c) - a(d)
= a(b + c - d)


2,
8a - 12b
= 4(2a) - 4(3b)
= 4(2a - 3b)


3,
9ap + 15aq
= 3a(3p + 5q)


4,
a2 + 4a
= a(a) + a(4)
= a(a + 4)


5,
4b2 + 6b
= 2b(2b) + 2b(3)
= 2b(2b + 3)


6,
3c - 9c3
= 3c(1) - 3c(3c2)
= 3c(1 - 3c2)


7,
Put u = a + b
y(a + b) - x(a + b)
= yu - xu
= (y - x)u
= (y - x)(a + b)


8,
Put u = a + b
(a + b)2 - 2(a + b)
= u2 - 2u
= u(u) - u(2)
= u(u - 2)
= (a + b)(a + b - 2)


9,
Let a - b = u, then b - a = -u
2x(a - b) + 3y(b - a)
= 2xu + 3y(-u)
= u(2x) - u(3y)
= u(2x - 3y)
= (a - b)(2x - 3y)


10,
ab2 + 3ab + a2b
= ab(b) + ab(3) + ab(a)
= ab(b + 3 + a)
= ab(a + b + 3)


11,
2b + 4b2 - 16b3
= 2b(1) + 2b(2b) - 2b(8b2)
= 2b(1 + 2b - 8b2)
= 2b(1 + 4b)(1 - 2b)


12,
7a4 - 14a3 + 28a
= 7a(a3) - 7a(2a2) + 7a(4)
= 7a(a3 - 2a2 + 4)


13,
Put a - b = u, then b - a = -u
p(a - b) + q(a - b) + r(b - a)
= pu + qu + r(-u)
= u(p) + u(q) - u(r)
= u(p + q - r)


14,
Put u = a + b - c
2p(a + b - c) - 3q(a + b - c)
= 2pu - 3qu
= u(2p) - u(3q)
= u(2p - 3q)
= (a + b - c)(2p - 3q)


15,
Put u = 2a - b, then 2u = 4a - 2b
p(2a - b) + q(4a - 2b)
= pu + q(2u)
= u(p) + u(2q)
= u(p + 2q)
= (2a - b)(p + 2q)


16,
ax - ay + bx - by
= a(x - y) + b(x - y)
= (a + b)(x - y)


17,
px + py - qx - qy
= p(x + y) - q(x + y)
= (p - q)(x + y)


18,
3x + 2y - 12xz - 8yz
= 1(3x) + 1(2y) - 4z(3x) - 4z(2y)
= 1(3x + 2y) - 4z(3x + 2y)
= (1 - 4z)(3x + 2y)


19,
xy - 4y - 5x + 20
= y(x) - y(4) - 5(x) - 5(-4)
= y(x - 4) - 5(x - 4)
= (y - 5)(x - 4)


20,
a2 - ab + ac - bc
= a(a) - a(b) + c(a) - c(b)
= a(a - b) + c(a - b)
= (a + c)(a - b)


21,
ab - a - pb + p
= a(b) - a(1) - p(b) - p(-1)
= a(b - 1) - p(b - 1)
= (a - p)(b - 1)


22,
(a + b)p- 2a - 2b
= (a + b)p - 2(a) - 2(b)
= (a + b)p - (a + b)2
= (a + b)(p - 2)


23
Put u = a - b, then -u = b - a
p(a - b) -q(b - a)
= pu - q(-u)
= p(u) + q(u)
= (p + q)u
= (p + q)(a - b)