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222-9+11+12:2*14+14 = ? ( )

## Toán Lớp 8: 6 (a+b) ^3=a^3+b^3+3ab (a+b) 7 (a – b) ^3= a^3-b^3+3ab(a-b) 8 x^3-y^3+xy(x-y)=(x-y) (x+y)^2 9 x^3+y^3-xy(x+y) = (x+y) (x-y)^2

Toán Lớp 8: 6 (a+b) ^3=a^3+b^3+3ab (a+b)
7 (a – b) ^3= a^3-b^3+3ab(a-b)
8 x^3-y^3+xy(x-y)=(x-y) (x+y)^2
9 x^3+y^3-xy(x+y) = (x+y) (x-y)^2

1. ***Lời giải***
6)
Chứng minh: (a+b) ^3=a^3+b^3+3ab (a+b)
Ta có: (a+b) ^3=a^3+3a^2b+3ab^2+b^3
=a^3+b^3+(3a^2b+3ab^2)
=a^3+b^3+3ab(a+b)
Vậy (a+b) ^3=a^3+b^3+3ab (a+b)
7)
Chứng minh: (a – b) ^3= a^3-b^3+3ab(b-a)
Ta có: (a – b) ^3=a^3-3a^2b+3ab^2-b^3
=a^3-b^3+(-3a^2b+3ab^2)
=a^3-b^3+3ab(b-a)
Vậy (a – b) ^3= a^3-b^3+3ab(b-a)
8)
Chứng minh: x^3-y^3+xy(x-y)=(x-y) (x+y)^2
Ta có: (x-y) (x+y)^2=(x-y) (x+y)(x+y)
=(x^2-y^2)(x+y)
=x^2(x+y)-y^2(x+y)
=x^3+x^2y-xy^2-y^3
=x^3-y^3+(x^2y-xy^2)
=x^3-y^3+xy(x-y)
Vậy x^3-y^3+xy(x-y)=(x-y) (x+y)^2
9)
Chứng minh: x^3+y^3-xy(x+y) = (x+y) (x-y)^2
Ta có: (x+y) (x-y)^2=(x+y)(x-y)(x-y)
=(x^2-y^2)(x-y)
=x^2(x-y)-y^2(x-y)
=x^3-x^2y-xy^2+y^3
=x^3+y^3+(-x^2y-xy^2)
=x^3+y^3-xy(x+y)
Vậy x^3+y^3-xy(x+y) = (x+y) (x-y)^2

→ \text{Chứng minh:}
6)
(a+b)^3 = a^3+b^3+2ab(a+b)
\text{·Ta có:}
VT = (a+b)^3
= a^3+3.a^2b+3.a.b^2+b^3
= (a^3+b^3)+(3a^2b+3ab^2)
= (a^3+b^3)+3ab(a+b) = VP \text{(→đpcm)}
7)
(a-b)^3 = a^3-b^3+3ab(a-b)
\text{·Ta có:}
VT = (a-b)^3
= a^3-3.a^2b+3.ab^2-b^3
= (a^3-b^3)+(-3a^2b+3ab^2)
= (a^3+b^3)+3ab(-a+b)
= (a^3+b^3)+3ab(b-a) = VP \text{(→đpcm)}
8)
x^3-y^3+xy(x-y) = (x-y)(x+y)^2
\text{·Ta có:}
VT = x^3-y^3+xy(x-y)
= (x-y)(x^2+xy+y^2)+xy(x-y)
= (x-y)(x^2+xy+y^2+xy)
= (x-y)(x^2+2xy+y^2)
= (x-y)(x+y)^2 = VP \text{(→đpcm)}
9)
x^3+y^3-xy(x+y) = (x+y)(x-y)^2
\text{·Ta có:}
VT = x^3+y^3-xy(x+y)
= (x+y)(x^2-xy+y^2)-xy(x+y)
= (x+y)(x^2-xy+y^2-xy)
= (x+y)(x^2-2xy+y^2)
= (x+y)(x-y)^2 = VP \text{(→đpcm)}