Math(因式分解)

(1) Let u = x + 1; v = y - 1
6(x+1)^2+5(x+1)(y-1)-6(y-1)^2
= 6u^2 + 5uv - 6v^2
= 6u^2 + 9uv - 4uv - 6v^2
= 3u(2u + 3v) - 2v(2u + 3v)
= (3u - 2v)(2u + 3v)
= [3(x + 1) - 2(y - 1)][2(x + 1) + 3(y - 1)]
= (3x - 2y + 5)(2x + 3y - 1)
(2) (3p - 1)(p + 5) - (p^2 + 15p + 1)
= 3p^2 + 15p - p - 5 - p^2 - 15p - 1
= 2p^2 - p - 6
= 2p^2 - 4p + 3p - 6
= 2p(p - 2) + 3(p - 2)
= (2p + 3)(p - 2)
(3) 9(3r + 1)^2 - 24(3r + 1) + 16
Let u = 3r + 1
= 9u^2 - 24u + 16
= 9u^2 - 12u - 12u + 16
= 3u(3u - 4) - 4(3u - 4)
= (3u - 4)^2
= [3(3r + 1) - 4]^2
= (9r - 1)^2

1.
6(x+1)2+5(x+1)(y-1)-6(y-1)2
=[3(x+1)-2(y-1)] [2(x+1)+3(y-1)]
=(3x-2y+5)(2x+3y-1)

2.
(3p-1)(p+5)-(p2+15p+1)
=(3p2+14p-5)-(p2+15p+1)
=2p2-p-6
=(2p+3)(p-2)

3.
9(3r+1)2-24(3r+1)+16
=[3(3r+1)-4]2
=(9r-1)2