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(a + b + c)^2 + (a - b - c)^2 +( b - c - a) ^2 + (c - a - b)^2
= (a + b + c)^2 + (a + b - c)^2 + (a - b - c)^2 + (a - b + c)^2
= (a + b)^2 + 2c(a + b) + c^2 + (a + b)^2 - 2c(a + b) + c^2 +
(a - b)^2 - 2c(a - b) + c^2 + (a - b)^2 + 2c(a - b) +c^2
= 2(a + b)^2 + 2c^2 + 2(a - b)^2 + 2c^2
= 2[(a + b)^2 + (a - b)^2] + 4c^2
=2(2a^2 + 2b^2) + 4c^2
= 4(a^2 + b^2 + c^2)
a) \(\left(m+n\right)^2-\left(m-n\right)^2+\left(m+n\right)\left(m-n\right)\)
\(=\left(m+n+m-n\right)\left(m+n-m+n\right)+m^2-n^2\)
\(=m^2-n^2+4mn\)
b) \(\left(a+b\right)^3+\left(a-b\right)^3-2a^3\)
\(=\left(a+b-a+b\right)\left[\left(a+b\right)^2-\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]-2a^3\)
\(=2b\left[a^2+2ab+b^2-a^2+b^2+a^2-2ab+b^2\right]-2a^3\)
\(=2b\left(a^2+3b^2\right)-2a^3\)
\(=2a^2b+6b^3-2a^3.\)
Tương tự áp dụng các HĐT.
a) \(\left(m+n\right)^2-\left(m-n\right)^2=\left[\left(m+n\right)-\left(m-n\right)\right]\left[\left(m+n\right)+\left(m-n\right)\right]=\left(2n\right)\left(2m\right)=4mn\)\(\left(m+n\right)\left(m-n\right)=m^2-n^2\)
A=\(4mn+m^2-n^2\) tối giản rồi
b)
\(\left(a+b\right)^3+\left(a-b\right)^3=\left[\left(a+b\right)+\left(a-b\right)\right]^3-3\left(a+b\right)\left(a-b\right)\left[\left(a+b\right)+\left(a-b\right)\right]=8a^3-3.2a.\left(a^2-b^2\right)\)B=\(8a^3-3.2a.\left(a^2-b^2\right)-2a^3=6a\left[a^2-\left(a^2-b^2\right)\right]=6ab^2\)
\(\left(a^2+b^2+c^2\right)-\left(a^2+b^2+c^2\right)^2\)
\(=\left(a^2+b^2+c^2\right)\left(1-a^2+b^2+c^2\right)\)
\(=\left(a^2+b^2+c^2\right)\left[\left(1-a\right)\left(1+a\right)+b^2+c^2\right]\)
mik làm thế này k bít có đúng k
Bài làm
( a2 + b2 + c2 ) - ( a2 + b2 + c2 )2
= ( a2 + b2 + c2 ) - ( a2 + b2 + c2 + a2b2 + a2c2 + b2c2 )
= a2 + b2 + c2 - a2 - b2 - c2 - a2b2 - a2c2 - b2c2
= -( a2b2 + a2c2 + b2c2 )
a: \(=a^2+2a\left(b-c\right)+\left(b-c\right)^2+a^2-2a\left(b-c\right)+\left(b-c\right)^2-2\left(b-c\right)^2\)
\(=2a^2+2\left(b-c\right)^2-2\left(b-c\right)^2=2a^2\)
b: \(=a^2+2a\left(b+c\right)+\left(b+c\right)^2+a^2-2a\left(b+c\right)+\left(b+c\right)^2+\left(b-c-a\right)^2+\left(c-a-b\right)^2\)
\(=2a^2+2\left(b+c\right)^2+\left(a-b+c\right)^2+\left(a+b-c\right)^2\)
\(=2a^2+2\left(b+c\right)^2+a^2-2a\left(b-c\right)+\left(b-c\right)^2+a^2+2a\left(b-c\right)+\left(b-c\right)^2\)
\(=2a^2+2\left(b+c\right)^2+2a^2+2\left(b-c\right)^2\)
\(=4a^2+2\left(b^2+2bc+c^2+b^2-2bc+c^2\right)\)
\(=4a^2+4b^2+4c^2\)
\(1.a\left(a+2b\right)^3-b\left(2a+b\right)^3\)
=\(a\left(a^3+6a^2b+12ab^2+8b^3\right)-b\left(8a^3+12a^2b+6ab^2+b^3\right)\)
=\(a^4+6a^3b+12a^2b^2+8ab^3-8a^3b-12a^2b^2-6ab^3-b^4\)
=\(a^4-b^4\)=\(\left(a^2-b^2\right)\left(a^2+b^2\right)\)
MK DANG CAN GAP LAM .AI BIET THI GIUP VOI
A=( a2 + b2 + c2 )2 - ( a2 - b2 + c2 )2=(a^2+b^2+c^2-a^2+b^2-c^2)(a^2+b^2+c^2+a^2-b^2+c^2)=2(b^2+c^2).2.(a^2+c^2)=4(b^2+c^2)(a^2+c^2)
B=( a + b + c )2 + ( a + b - c)2 - 2 ( a + b )2=a^2+b^2+c^2+2ab+2bc+2ac+a^2+b^2+c^2-2ab-2bc+2ac-2a^2-2ab-2b^2=b^2+2bc+c^2=(b+c)^2
câu C làm tương tự