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Toán Lớp 8: chung minh rang a, a^3-b^3=(a-b)^3+3ab(a-b) b, (a-b+c)^2=a^2+b^2+c^2-2ab-2bc+2ca c,(a-b-c)^2=a^2+b^2+c^2-2ab+2bc-2ca

Home/ Toán Lớp 8: chung minh rang a, a^3-b^3=(a-b)^3+3ab(a-b) b, (a-b+c)^2=a^2+b^2+c^2-2ab-2bc+2ca c,(a-b-c)^2=a^2+b^2+c^2-2ab+2bc-2ca

Toán Lớp 8: chung minh rang a, a^3-b^3=(a-b)^3+3ab(a-b) b, (a-b+c)^2=a^2+b^2+c^2-2ab-2bc+2ca c,(a-b-c)^2=a^2+b^2+c^2-2ab+2bc-2ca

Thu Giang Tháng Mười 23, 2022 Toán học 1 Comment 0 views

Toán Lớp 8: chung minh rang
a, a^3-b^3=(a-b)^3+3ab(a-b)
b, (a-b+c)^2=a^2+b^2+c^2-2ab-2bc+2ca
c,(a-b-c)^2=a^2+b^2+c^2-2ab+2bc-2ca

Comments ( 1 )

ngocle44
23 Tháng Mười, 2022 at 12:25 sáng

Reply

a)

Ta có :

(a-b)^3 + 3ab (a-b)

= [a^3 – b^3 – 3ab (a-b)] + 3ab (a-b)

= a^3 – b^3 – 3ab (a-b) + 3ab (a-b)

= a^3-b^3

Vậy a^3-b^3=(a-b)^3 + 3ab(a-b)

b)

Ta có :

(a-b+c)^2

= [ (a-b) + c]^2

= (a-b)^2 + 2c (a-b) + c^2

= (a^2-2ab+b^2) + 2ac – 2bc + c^2

= a^2 + b^2 + c^2 – 2ab – 2bc + 2ca

Vậy (a-b+c)^2= a^2 + b^2 + c^2 – 2ab – 2bc + 2ca

c)

Ta có :

(a-b-c)^2

= [(a-b)-c]^2

= (a-b)^2 – 2c (a-b) + c^2

= a^2 – 2ab + b^2 – 2ac + 2bc + c^2

= a^2 + b^2 +c^2 – 2ab + 2bc – 2ca

Vậy (a-b-c)^2 = a^2 + b^2 +c^2 – 2ab + 2bc – 2ca

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