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a, \(4\left(x+y+z\right)^2-9\left(x-y-z\right)^2\)
\(=\left[2\left(x+y+z\right)\right]^2-\left[3\left(x-y-z\right)\right]^2\)
\(=\left[2x+2y+2z\right]^2-\left[3x-3y-3z\right]^2\)
\(=\left[\left(2x+2y+2z\right)-\left(3x-3y-3z\right)\right].\left[\left(2x+2y+2z\right)+\left(3x-3y-3z\right)\right]\)
\(=\left(-x+5y+5z\right)\left(5x-y-z\right)\)
b, \(25\left(x-3y\right)^2-4\left(x+3y\right)^2\)
\(=\left[5\left(x-3y\right)\right]^2-\left[2\left(x+3y\right)\right]^2\)
\(=\left[5x-15y\right]^2-\left[2x+6y\right]^2\)
\(=\left[5x-15y-2x-6y\right].\left[5x-15y+2x+6y\right]\)
\(=\left(3x-21y\right)\left(7x-9y\right)\)
\(=3\left(x-7y\right)\left(7x-9y\right)\)
Chúc bạn học tốt.
a) \(x^2-y^2-3x+3y\)
\(=\left(x-y\right)\left(x+y\right)-3\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-3\right)\)
b) \(2x+2y-x^2+y^2\)
\(=2\left(x+y\right)-\left(x^2-y^2\right)\)
\(=2\left(x+y\right)-\left(x-y\right)\left(x+y\right)\)
\(=\left(x+y\right)\left(2-x+y\right)\)
c) \(x^2-16+y^2+2xy\)
\(=x^2+y^2+2xy-16\)
\(=\left(x+y\right)^2-16\)
\(=\left(x+y+4\right)\left(x+y-4\right)\)
a) \(x^2-y^2-3x+3y\)
\(=\left(ax+y\right)\left(ax-y\right)-3.\left(x-y\right)\)
b) \(2x+2y-x^2+y^2\)
\(=2\left(x+y\right)-\left(x+y\right)\left(x-y\right)\)
c) \(x^2-16+y^2+2xy\)
\(=\left(x+y\right)\left(x-y\right)+2xy-16\)
2x(x-2)+2y(x-2)= (x-2)(2x+2y)=2(x-2)(x+y)
b,2(xy+xyz-2x-2z)
c, 3(x^2-xy-x-y)
a) Ta có : 2x2 - 4x + 2xy - 4y
= 2x(x - 2) + 2y(x - 2)
= (x - 2)(2x + 2y)
= 2(x - 2)(x + y)
a: \(x^2-y^2-x-y\)
\(=\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-1\right)\)
f: \(x^3-5x^2-5x+1\)
\(=\left(x+1\right)\left(x^2-x+1\right)-5x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-6x+1\right)\)
a: \(x^2+4xy+y^2\)
\(=x^2+4xy+4y^2-3y^2\)
\(=\left(x+2y-y\sqrt{3}\right)\left(x+2y+y\sqrt{3}\right)\)