(a+b+c)^2+(a+b-c)^2 -4c^2
mong mn giúp đỡ :<
(a+b+c)^2+(a+b-c)^2 -4c^2 mong mn giúp đỡ :<
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(a+b+c)^2+(a+b-c)^2 -4c^2
mong mn giúp đỡ :<
Helga
Đáp án:
Ta có :
`(a + b + c)^2 + (a + b – c)^2 – 4c^2`
`= (a + b + c)^2 + [(a + b – c)^2 – (2c)^2]`
`= (a + b + c)^2 + (a + b – c – 2c)(a + b – c + 2c)`
`= (a + b + c)^2 + (a + b – 3c)(a + b + c)`
`= (a + b + c)(a + b + c + a + b – 3c)`
`= (a + b + c)(2a + 2b – 2c)`
`= 2(a + b + c)(a + b – c)`
Giải thích các bước giải:
Nho
`(a+b+c)^2+(a+b-c)^2-4c^2`
`=a^2+b^2+c^2+2ab+2bc+2ac+a^2+b^2+c^2 +2ab-2ac-2bc-4c^2`
`=2a^2+2b^2-2c^2+4ab`
`=2(a^2+b^2+2ab-c^2)`
`=2.[(a+b)^2-c^2]`
`=2(a+b+c)(a+b-c)`