11. a) (x+2y)2
=x2+2.x.2y+(2y)2
=x2+4xy+4y2
b) (x-3y)(x+3y)
=x2-y2
c) (5-x)2
=52-2.5.x+x2
=25-10x+x2
12. a) (x-1)2
=x2-2.x.1+12
=x2-2x+1
b) (3-y)2
=32-2.3.y+y2
=9-6y+y2
c) (x-1/2)2
=x2-2.x.1/2+1/22
=x2-2x+1/4
13. a) x2+6x+9
=x2+2.x.3+32
=(x+3)2
b) x2+x+1/4
=x2+2.x.1/4+1/22
=(x+1/2)2
c) 2xy2+x2y4+1
=(xy2)2+2xy2+12
=(xy2+1)2
14. a) (x+y)2+(x-y)2
=2(x2+y2)
b) 2(x-y)(x+y)+(x+y)2+(x-y)2
=(x+y)2+2.(x-y)2+(x-y)2
=( x+y+x-y)2
=(2x)2
=4x2
c) (x-y+z)2+(z-y)2+2(x-y+z)(y-z)
=(x-y+z)2+2(x-y+z)(y-z)+
(z-y)2
=[(x-y+z)-(z-y)]2
=(x-y+z-z+y)2
=x2
16. a) x2-y2
=(x+y)(x-y)
Tại x=87;y=13
=(87+13)(87-13)
=100.47
=4700
b) x3-3x2+3x-1
=(x-1)3
Tại x=101
=(101-1)3
=1003
=1000000
c) x3+9x2+27x+27
= (x+3)3
Tại x=97
=(97+3)3
=1003
=1000000
17. a) (a+b)(a2-ab+b2)+(a-b)(a2+ab+b2)=2a3
óa3-a2b+ab2+a2b-ab2+b3+a3+a2b+ab2-a2b-ab2-b3=2a3
ó2a3=2a3
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