7 hằng đẵng thức đã học:
1)
(A+B)2
= A2+2AB+B2
2)
(A-B)2
= A2-2AB+B3
3)
A2-B2
= (A+B)(A-B)
4)
(A+B)3
= A3+3A2B+3AB2+B3
5)
(A-B)3
= A3-3A2B+3AB2-B3
6)
A3+B3
= (A+B)(A2+AB+B2)
7)
A3-B3
= (A-B)(A2+AB+B2)
33. a) (2+xy)2
=22+2.2xy+x2y2
=4+4xy+x2y2
b) (5-3x)2
=52-2.5.3x+(3x)2
=25-30x+9x2
c) (5x-1)3
=(5x)3-3.(5x)2.1+3.5x.12-13
=125x3-75x2+15x-1
d) (5-x2)(5+x2)
=52-(x2)2
e) (2x-y)(4x2+2xy+y2)
=(2x)3-y3
f) (x+3)(x2-3x+9)
=x3+33
34. a) (a+b)2-(a-b)2
=a2+2ab+b2-a2+2ab-b2
=4ab
b) (x+y+z)-2(x+y+z)(x+y)+(x+y)2
=[(x+y+z)-(x+y)]2
=(x+y+z-x-y)
=z2
c) (a+b)3-(a-b)3-2b3
=a+3a2b+3ab3+b3-a3+3a2b-3ab2+b3+2b3
=3a2b+4b3
35. a) 342+662+68.66
=342+2.34.66+662
=(34+66)2
=1002=10000
b) 742+242-48.74
=742-2.74.24+242
=(74-24)2
=502=2500
36. a) x2+4x+4
tại x=98
=x2+2.1x.2+22
=(x+2)2
Tại x=98
=(98+2)2
=1002
=10000
b) x3+3x2+3x+1 tại x=90
=x3+3.(1x)2.1+3.1x.12+13
=(x+1)3
Tại x=99
=(99+1)3
=1003
=1000000
37. a) (x-y)(x2+xy+y2)=x3-y3
b) (x+y)(x-y)=x2-y2
c) x2-2xy+y2=(x-y)2
d) (x+y)2=x2+2xy+y2
e) (x+y)(x2-xy+y2)=x3+y3
f) y3+3xy2+3x2y+x3=(x+y)3
g) (x-y)3=x3-3x2y+3xy2-y3
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