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29 tháng 10 2016
\(\left(a+b+c\right)^2+\left(a+b-c\right)^2-4c\)
\(=\left(a+b\right)^2+2.c\left(a+b\right)+c^2+\left(a+b\right)^2-2.c\left(a+b\right)+c^2-4c^2\)
\(=a^2+2ab+b^2+2ca+2cb+c^2+a^2+2ab+b^2-2ca-2cb+c^2-4c^2\)
\(=2a^2+4ab+2b^2-2c^2\)
\(=2\left(a^2+2ab+b^2-c^2\right)\)
\(=2\left[\left(a+b\right)^2-c^2\right]\)
\(=2\left(a+b+c\right)\left(a+b-c\right)\)
28 tháng 9 2018
\(\left(a+b\right)\left(a^2-b^2\right)+\left(b+c\right)\left(b^2-c^2\right)+\left(c+a\right)\left(c^2-a^2\right)\)
\(=\left(a+b\right)\left(a^2-b^2\right)-\left(b+c\right)\left[c^2-a^2+a^2-b^2\right]+\left(c+a\right)\left(c^2-a^2\right)\)
\(=\left(a+b\right)\left(a^2-b^2\right)-\left(b+c\right)\left(c^2-a^2\right)-\left(b+c\right)\left(a^2-b^2\right)+\left(c+a\right)\left(c^2-a^2\right)\)
\(=\left(a^2-b^2\right)\left(a+b-b-c\right)+\left(c^2-a^2\right)\left(c+a-b-c\right)\)
\(=\left(a-b\right)\left(a+b\right)\left(a-c\right)+\left(c-a\right)\left(c+a\right)\left(a-b\right)\)
\(=\left(a-b\right)\left(a-c\right)\left(a+b-c-a\right)\)
\(=\left(a-b\right)\left(a-c\right)\left(b-c\right)\)
Chúc bạn học tốt.
N
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11 tháng 12 2017
\(P=a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)\)
\(P=a^2b-a^2c+b^2c-b^2a+c^2\left(a-b\right)\)
\(P=\left(a^2b-b^2a\right)-\left(a^2c-b^2c\right)+c^2\left(a-b\right)\)
\(P=ab\left(a-b\right)-c\left(a^2-b^2\right)+c^2\left(a-b\right)\)
\(P=ab\left(a-b\right)-c\left(a-b\right)\left(a+b\right)+c^2\left(a-b\right)\)
\(P=\left(a-b\right)\left[ab-c\left(a+b\right)+c^2\right]\)
\(P=\left(a-b\right)\left(ab-ca-cb+c^2\right)\)
\(P=\left(a-b\right)\left[\left(ab-cb\right)-\left(ca-c^2\right)\right]\)
\(P=\left(a-b\right)\left[b\left(a-c\right)-c\left(a-c\right)\right]\)
\(P=\left(a-b\right)\left(a-c\right)\left(b-c\right)\)
\(\left(a+b+c\right)^2+\left(a+b-c\right)^2-4c^2\)
\(=\left(a+b+c\right)^2+\left(a+b-c+2c\right)\left(a+b-c-2c\right)\)
\(=\left(a+b+c\right)^2+\left(a+b+c\right)\left(a+b-3c\right)\)
\(=\left(a+b+c\right)\left(a+b+c+a+b-3c\right)\)
\(=\left(a+b+c\right)\left(2a+2b-2c\right)\)
\(=2\left(a+b+c\right)\left(a+b-c\right)\)