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a) \(x\left(x+2\right)+y\left(y-2\right)-2xy+37\)
\(=x^2+2x+y^2-2y-2xy+37\)
\(=\left(x^2-2xy+y^2\right)+2x-2y+37\)
\(=\left(x-y\right)^2+2\left(x-y\right)+37\)
\(=7^2+2.7+34\)
\(=100\)
b) \(x^2\left(x+1\right)-y^2\left(y-1\right)+xy-3xy\left(x-y+1\right)-95\)
\(=x^3+x^2-y^3+y^2+xy-3xy-3xy\left(x-y\right)-95\)
\(=x^3+x^2-y^3+y^2-2xy-3xy\left(x-y\right)-95\)
\(=\left(x-y\right)^3+\left(x-y\right)^2-95\)
\(=7^3+7^2-95\)
\(=297\)
1a) (x - 2y) (x2 - 2xy + y2)
= (x - 2y) (x - y)2
= x2 - xy - 2xy + 2y2
= (x2 - xy) - (2xy - 2y2)
= x (x - y) - 2y (x - y)
= (x - y) (x - 2y)
2a) x (x - 3) - y (3 - x)
= x (x - 3) + y (x - 3)
= (x - 3) (x + y)
b) 3x2 - 5x - 3xy + 5y
= (3x2 - 3xy) - (5x - 5y)
= 3x (x - y) - 5 (x - y)
= (x - y) (3x - 5)
3) 12x (3 - 4x) + 7 (4x - 3) = 0
12x (3 - 4x) - 7 (3 - 4x) = 0
(3 - 4x) (12x - 7) = 0
=> 3 - 4x = 0 hoặc 12x - 7 = 0
* 3 - 4x = 0 => x = \(\frac{3}{4}\)
* 12x - 7 = 0 => x = \(\frac{7}{12}\)
Vậy x =\(\frac{3}{4}\)hoặc x =\(\frac{7}{12}\)
c) hang dang thuc ( x -y+z)^2
o duoi phan h hang dang thuc luon
a) phan h nhan tu ra sao cho co tử la (x-1)(3x^2 -4x +1)
mau la (x-1)(2x^2 -x-3)
b ) k nhin dc de
giải :
\(x^3-3xy\left(x-y\right)-y^3-x^2+2xy-y^2\)
= \(x^3-3x^2y+3xy^2-y^3-x^2+2xy-y^2\)
= \(\left(x^3-3x^2y+3xy^2-y^3\right)-\left(x^2-2xy+y^2\right)\)
= \(\left(x-y\right)^3-\left(x-y\right)^2\)