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10 tháng 7 2019

mk ko bt

29 tháng 6 2017

a) (a+b+c)^2 + (a+b-c)^2 - 4c^2

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

\(=\left(a+b+c\right)^2+\left(a+b-c+2c\right)\left(a+b-c-2c\right)\)

\(=\left(a+b+c\right)^2+\left(a+b+c\right)\left(a+b-3c\right)\)

\(=\left(a+b+c\right)\left(a+b+c+a+b-3c\right)\)

\(=\left(a+b+c\right)\left(2a+2b-2c\right)\)

\(=2\left(a+b+c\right)\left(a+b-c\right)\)

b) 4a^2b^2 - (a^2+b^2-c^2)^2

\(=\left(2ab\right)^2-\left(a^2+b^2-c^2\right)^2=\left(2ab+a^2+b^2-c^2\right)\left(2ab-a^2-b^2+c^2\right)\)

\(=\left[\left(a^2+2ab+b^2\right)-c^2\right]\left[c^2-\left(a^2-2ab+b^2\right)\right]\)

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

\(=\left(a+b+c\right)\left(a+b-c\right)\left(c+a-b\right)\left(c-a+b\right)\)

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

\(=ab^3-ac^3+bc^3-a^3b+a^3c-b^3c\)

\(=a^3\left(c-b\right)+bc\left(c-b\right)\left(c+b\right)-a\left(c-b\right)\left(c^2+bc+b^2\right)\)

\(=a^3\left(c-b\right)+\left(c-b\right)\left(bc^2+b^2c\right)-\left(c-b\right)\left(ac^2+abc+ab^2\right)\)

\(=\left(c-b\right)\left(a^3+bc^2+b^2c-ac^2-abc-ab^2\right)\)

29 tháng 6 2017

a) (a+b+c)^2 + (a+b-c)^2 - 4c^2

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

\(=\left(a+b+c\right)^2+\left(a+b-c+2c\right)\left(a+b-c-2c\right)\)

\(=\left(a+b+c\right)^2+\left(a+b+c\right)\left(a+b-3c\right)\)

\(=\left(a+b+c\right)\left(a+b+c+a+b-3c\right)\)

\(=\left(a+b+c\right)\left(2a+2b-2c\right)\)

\(=2\left(a+b+c\right)\left(a+b-c\right)\)

b) 4a^2b^2 - (a^2+b^2-c^2)^2

\(=\left(2ab\right)^2-\left(a^2+b^2-c^2\right)^2=\left(2ab+a^2+b^2-c^2\right)\left(2ab-a^2-b^2+c^2\right)\)

\(=\left[\left(a^2+2ab+b^2\right)-c^2\right]\left[c^2-\left(a^2-2ab+b^2\right)\right]\)

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

\(=\left(a+b+c\right)\left(a+b-c\right)\left(c+a-b\right)\left(c-a+b\right)\)

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

\(=ab^3-ac^3+bc^3-a^3b+a^3c-b^3c\)

\(=a^3\left(c-b\right)+bc\left(c-b\right)\left(c+b\right)-a\left(c-b\right)\left(c^2+bc+b^2\right)\)

\(=a^3\left(c-b\right)+\left(c-b\right)\left(bc^2+b^2c\right)-\left(c-b\right)\left(ac^2+abc+ab^2\right)\)

\(=\left(c-b\right)\left(a^3+bc^2+b^2c-ac^2-abc-ab^2\right)\)

31 tháng 10 2015

\(ab\left(a-b\right)+bc\left(b-c\right)+ca\left(c-a\right)\)

\(=ab\left(a-b\right)+bc\left(b-c\right)-ca\left(a-c\right)\)

\(=ab\left(a-b\right)+bc\left(b-c\right)-ca\left(a-b+b-c\right)\)

\(=ab\left(a-b\right)+bc\left(b-c\right)-ca\left(a-b\right)-ca\left(b-c\right)\)

\(=\left(a-b\right)\left(ab-ca\right)+\left(b-c\right)\left(bc-ca\right)\)

\(=\left(a-b\right)a\left(b-c\right)+\left(b-c\right)c\left(b-a\right)\)

\(=\left(a-b\right)a\left(b-c\right)-\left(b-c\right)c\left(a-b\right)\)

\(=\left(a-b\right)\left(b-c\right)\left(a-c\right)\)

mình làm vội, có chỗ nào sai bạn thông cảm nha

15 tháng 7 2017

\(D=a^3\left(b-c\right)+b^3\left(c-a\right)+c^3\left(a-b\right)\)

\(D=a^3\left(b-c\right)+\left[b^3\left(c-a\right)+c^3\left(a-b\right)\right]\)

\(D=a^3\left(b-c\right)\left(b^3c-ab^3+ac^3-bc^3\right)\)

\(D=a^3\left(b-c\right)\left[\left(b^3c-bc^3\right)-\left(ab^3-ac^3\right)\right]\)

\(D=a^3\left(b-c\right)\left[bc\left(b^2-c^2\right)-a\left(b^3-c^3\right)\right]\)

\(D=a^3\left(b-c\right)\left[bc\left(b-c\right)\left(b+c\right)-a\left(b-c\right)\left(b^2+bc+c^2\right)\right]\)

\(D=\left(b-c\right)\left[a^3+bc\left(b+c\right)-a\left(b^2+bc+c^2\right)\right]\)

\(D=\left(b-c\right)\left(a^3+b^2c+bc^2-ab^2-abc-ac^2\right)\)

\(D=\left(b-c\right)\left[\left(b^2c-ab^2\right)+\left(bc^2-abc\right)-\left(ac^2-a^3\right)\right]\)

\(D=\left(b-c\right)\left[b^2\left(c-a\right)+bc\left(c-a\right)-a\left(c^2-a^2\right)\right]\)

\(D=\left(b-c\right)\left[b^2\left(c-a\right)+bc\left(c-a\right)-a\left(c-a\right)\left(c+a\right)\right]\)

\(D=\left(b-c\right)\left(c-a\right)\left[b^2+bc-a\left(c+a\right)\right]\)

\(D=\left(b-c\right)\left(c-a\right)\left(b^2+bc-ac-a^2\right)\)

\(D=\left(b-c\right)\left(c-a\right)\left[\left(bc-ac\right)+\left(b^2-a^2\right)\right]\)

\(D=\left(b-c\right)\left(c-a\right)\left[c\left(b-a\right)+\left(b-a\right)\left(b+a\right)\right]\)

\(D=\left(b-c\right)\left(c-a\right)\left(b-a\right)\left(c+b+a\right)\)

\(D=\left(a-b\right)\left(b-c\right)\left(a-c\right)\left(a+b+c\right)\)

Chúc bạn học tốt.

6 tháng 10 2018

Ai kb vs tui ko 

buồn quá hời!!

OLM đừng trừ điểm en nha 

đừng đưa nội quy mk bt hết oi

kiếm bn để chat thui!! ^.^