43. a) x2+6x+9
= x2+2.1x.3+32
= (x+3)2
b) 10x-25-x2
= -(x2-10x+25)
= -(x2-2.1x.5+52)
= -(x-5)2
c) 8x3-1/8
= 23x3-(1/2)3
= (2x)3-(1/2)3
= (2x-1/2)[(2x)2+2x.1/2+(1/2)2]
= (2x-1/2)(4x2+x+1/4)
d) 1/25x2-64y2
= (1/5x)2-(8y)2
= (1/5x+8y)(
1/5x-8y)
44. a) x3+1/27
= x3+(1/3)3
= (x+1/3)[(x2-x.1/3+(1/3)2]
= (x+1/3)(x2-1/3x+1/9)
b) (a+b)3-(a-b)3
= [(a+b)-(a-b)][(a+b)2+(a+b)(a-b)+(a-b)2]
= (a+b-a+b)(a2+2ab+b2+a2-b2+
a2-2ab+b2)
= 2b(3a2+b2)
c) (a+b)3+(a-b)3
= [(a+b)+(a-b)][(a+b)2+(a+b)(a-b)+(a-b)2]
= (a+b+a-b)(a2+2ab+b2-a2+b2+
a2-2ab+b2)
= 2a(a2+3b2)
d) 8x3+12x2y+6xy2+y3
= (2x)3+3.22.y+3.2.y2+y3
= (2x+y)3
e) –x3+9x2-27x+27
= -(x3-3.(1x)2.3+3.x.32-33)
= -(x-3)3
45. b) x2-x+1/4=0
ó
x2-2.x.1/2+(1/2)2=0
ó(x-1/2)2=
0
ó
x-1/2=0
ó x =
½
46. a) 732-272
=
(73-27)(73+27)
= 46.100
= 4600
b) 372-132
=
(37-13)(37+13)
= 24.50
= 10200
c) 20022-22
=
(2002-2)(2002+2)
= 2000.2004
= 4008000
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