急~因式分解!!數學高手入黎!!

(1)-p2q2+r4
(2)49a2-169b2c2
(3)-100s2+81t2
(4)72(x+y)2-8(x-y)2
(5)4c2-2c-9d2-3d
(6)75(s-3t)2-27(2s-5t)2
(7)12v-12v2-6u+3u2

(1)-p2q2+r4

= -(pq)²+r^4--------a²b²=(ab)²

= -(pq)²+(r²)²--------a^4=(a²)²

= (r²)²-(pq)²----------排好

=(r²+pq)(r²-pq)-----利用恆等式a²-b²=(a+b)(a-b)

(2)49a2-169b2c2

= (7a)²- (13bc)²

=(7a+13bc)(7a-13bc)-----利用恆等式a²-b²=(a+b)(a-b)

(3)-100s2+81t2

=- (10s)²+ (9t)²

= (9t)²-(10s)²

=(9t+10s)(9t-10s)----利用恆等式a²-b²=(a+b)(a-b)

(4)72(x+y)2-8(x-y)2

= 8[9(x+y)²-(x-y)²]--------------抽8

=8[(3(x+y)]²-(x-y)²

=8[3(x+y)+(x-y)][3(x+y)-(x-y)]

=8(3x+3y+x-y)(3x+3y-x+y)

=8(4x+2y)(4y+2x)

(5)4c²-2c-9d²-3d

=[(2c)²-2c]-(3d)²-3d

=2[c²-c]-3[d²-d]

(6)75(s-3t)2-27(2s-5t)2

=3[25(s-3t)²-9(2s-5t)²]

=3[5(s-3t)]²-[3(2s-5t)²]

=3(5(s-3t)+3(2s-5t))(5(s-3t)-3(2s-5t))

=3(5s-15t+6s-15t)(5s-15t-6s+15t)

=3(11s-30t)(-s)

=-3s(11s-30t)

(7)12v-12v²-6u+3u²

=3(4v-4v²-2u+u²)

=3(4v-2u)-(4v²+u²)

=6(2v-u)-[(2v)²+u²]