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4a^2-4ab+b^2-9a^2b^2
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LP
1
4 tháng 9 2021
\(4a^2b^2-\left(a^2+b^2-c^2\right)^2\)
\(=\left(2ab-a^2-b^2+c^2\right)\left(2ab+a^2+b^2-c^2\right)\)
\(=-\left[\left(a-b\right)^2-c^2\right]\left[\left(a+b\right)^2-c^2\right]\)
\(=-\left(a-b-c\right)\left(a-b+c\right)\left(a+b-c\right)\left(a+b+c\right)\)
G
10 tháng 8 2023
\(4a^2b^2-\left(a^2+b^2-c^2\right)^2\)
\(=4a^2b^2-2ab\left(a^2+b^2-c^2\right)+2ab\left(a^2+b^2-c^2\right)-\left(a^2+b^2-c^2\right)^2\)
\(=2ab\left[2ab-\left(a^2+b^2-c^2\right)\right]+\left(a^2+b^2-c^2\right)\left[2ab-\left(a^2+b^2-c^2\right)\right]\)
\(=\left(2ab+a^2+b^2-c^2\right)\left(2ab-a^2-b^2+c^2\right)\)
\(=\left(a^2+ab+ab+b^2-c^2\right)\left[c^2-\left(a^2-ab-ab+b^2\right)\right]\)
\(=\left[a\left(a+b\right)+b\left(a+b\right)-c^2\right]\left[c^2-\left(a\left(a-b\right)-b\left(a-b\right)\right)\right]\)
\(=\left[\left(a+b\right)^2-c^2\right]\left[c^2-\left(a-b\right)^2\right]\)
\(=\left[\left(a+b\right)^2-c\left(a+b\right)+c\left(a+b\right)-c^2\right]\left[c^2+c\left(a-b\right)-c\left(a-b\right)-\left(a-b\right)^2\right]\)
\(=\left[\left(a+b\right)\left(a+b-c\right)+c\left(a+b-c\right)\right]\left[c\left(c+a-b\right)-\left(a-b\right)\left(c+a-b\right)\right]\)
\(=\left(a+b+c\right)\left(a+b-c\right)\left(c+a-b\right)\left(c-a+b\right)\)
JP
1
LC
11 tháng 8 2015
=2ab.[a+2b]+c^2.[a+2b]- c.[a^2+4ab+4.b^2]
=.................................-c[a+2b]^2
=[a+2b].{2ab+c^2-ca-2bc]
=[a+2b]{ 2b.[a-c]-c.[a-c] }
=[a+2b].[a-c].[2b-c]
NC
2
30 tháng 6 2019
2a^2b + 4ab^2 -a^2c + ac^2 -4b^2c +2bc^2 - 4abc
= (2a^2b - 4abc + 2bc^2) + (4ab^2 - 4b^2c) - (a^2c - ac^2)
= 2b(a^2 - 2ac + c^2) + 4b^2(a - c) - ac(a - c)
= 2b(a - c)^2 + 4b^2(a - c) - ac(a - c)
= (a - c) [ 2b(a - c) + 4b^2 - ac ]
= (a - c) (2ab -2bc +4b^2 - ac)
= (a - c) [ (2ab - ac) + (4b^2 - 2bc) ]
= (a - c) [a(2b - c) + 2b(2b - c)]
= (a - c)(2b - c)(a + 2b)
30 tháng 6 2019
TL:
=\(\left(2a^2b-4bc+2bc^2\right)+\left(4ab^2-4b^2c\right)-\left(a^2c-ac2\right)\)
=\(2b\left(a^2-2c+c^2\right)+4b^2\left(a-c\right)-ac\left(a-c\right)\)
=\(2b\left(a-c\right)+4b^2\left(a-c\right)-ac\left(a-c\right)\)
=\(\left(a-c\right)\left(2b+4b^2-ac\right)\)
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Vậy......
G
1
PH
0
\(4a^2-4ab+b^2-9a^2b^2\)
\(=\left(2a-b\right)^2-9a^2b^2\)
\(=\left(2a-b-3ab\right)\left(2a-b+3ab\right)\)