a)5 a . ( a - 2 ) - a + 2
= 5a . ( a - 2 ) + (a - 2 )
= (5a + 1 ).(a - 2)
b)7. (a - 5) + 8a .(5 - a)
= 7. (a - 5) - 8a . (a - 5)
= (7 - 8a ).(a - 5)
c)25a2 - 4b2 + 4b - 1
= 25b2 - ( 4b2 + 4b - 1)
= 25b2 - ( 2b - 1)2
= ( 25b - 2b -1). ( 25b + 2b - 1)
= (23b - 1).( 27b - 1)
1/ Phân tích đa thức thành nhân tử:
a/ 5a.(a-2) - a+2 = 5a(a - 2) - (a - 2) = (a - 2)(5a - 1)
b/7.(a-5)+8a.(5-a) = 7(a - 5) - 8a(a - 5) = (a - 5) (7 - 8a)
c/ 25a2 -4b2 +4b -1 = 25a2 - (4b2 - 4b + 1) = 25a2 - (2b - 1)2
= (5a - 2b + 1)(5a +2b - 1)
d/6ax2 -36ax+54a = 6a( x2 - 6x + 9 ) = 6a(x - 3)2
e/ 2ax -3by+3bx-2ay = (2ax - 2ay) - (3by - 3bx)
= 2a(x - y) - 3b( y - x)
= 2a(x - y) + 3b(x - y)
= (2a +3b)(x - y)
f/ x2 +y2+2x-2y-2xy
= (x2 - 2xy + y2) + (2x - 2y)
= (x - y)2 + 2(x - y)
= (x - y)(2+ x - y)
g/ a2 -7a +10
= (a2 - 2.a.\(\frac{7}{2}\) + \(\frac{49}{4}\)) - \(\frac{9}{4}\)
= (a - \(\frac{7}{2}\))2 - \(\left(\frac{3}{2}\right)^2\)
= \(\left(a-\frac{7}{2}-\frac{3}{2}\right)\left(a-\frac{7}{2}+\frac{3}{2}\right)\)
= (a - 5). (a - 2)
d) 6ax2 - 36ax + 54a
= 6a. (x2 - 6x + 9)
= 6a. (x - 3)2
e) 2ax - 3by + 3bx - 2ay
= ( 2ax - 2ay) - ( 3by - 3bx )
= 2a.(x - y) - 3b. (x - y)
= (2a - 3b).(x - y)
f)x2 + y2 + 2x - 2y - 2xy
= (2x - 2y ). ( x2 - 2xy + y2 )
=2(x - y) . (x - y)2
= 2.(x - y)3