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TL:
\(4x^2-y^2+4x+1\)
\(=\left(2x-1\right)^2-y^2\)
\(=\left(2x-1+y\right)\left(2x-1-y\right)\)
\(x^3-x+y^3-y\)
\(=\left(x+y\right)\left(x^2-xy+x^2\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+x^2-1\right)\)
a) \(^{x^4-y^4}\)
\(=\left(x^2-y^2\right)\left(x^2+y^2\right)\)
\(=\left[\left(x-y\right).\left(x+y\right)\right].\left(x^2-y^2\right)\)
\(=\left(x-y\right).\left(x+y\right).\left(x^2-y^2\right)\)
c) \(\left(3x-2y\right)^2-\left(2x-3y\right)^2\)
\(=\left[\left(3x-2y\right)+\left(2x-3y\right)\right].\left[\left(3x-2y\right)-\left(2x-3y\right)\right]\)
\(=\left(3x-2y+2x-3y\right)\left(3x-2y-2x+3y\right)\)
b) \(x^2-3y^2\)
\(=\left(x-3y\right)\left(x+3y\right)\)
d) \(9\left(x-y\right)^2-4\left(x+y\right)^2\)
\(=9\left(x-y\right)^2+4\left(x-y\right)^2\)
\(=\left(x-y\right).\left(9+4\right)\)
\(=\left(x-y\right).13\)
\(=13\left(x-y\right)\)
f) \(x^3+27\)
\(=x^3+3^3\)
\(=\left(x+3\right)\left(x^2-x.3+3^2\right)\)
h) \(125x^3-1\)
\(=\left(5x\right)^3-1^3\)
\(=\left(5x-1\right)\left(5x^2+5x.1+1^2\right)\)
\(=\left(5x-1\right)\left(5x^2+5x+1\right)\)
\(a,x^4-y^4=\left(x^2+y^2\right)\left(x^2-y^2\right)=\left(x^2+y^2\right)\left(x+y\right)\left(x-y\right)\)
\(b,x^2-3y^2=\left(x+\sqrt{3}y\right)\left(x-\sqrt{3}y\right)\)
cn lại tg tự nha bn
a)\(x^2y-x^3-9y+9y\)
\(=x^2\left(y-x\right)-9\left(y-x\right)\)
\(=\left(x^2-9\right)\left(y-x\right)\)
\(=\left(x+3\right)\left(x-3\right)\left(y-x\right)\)
\(b,9x^2-1=\left(3x+1\right)\left(3x-1\right)\)
\(c,\left(x-y\right)4-4=\left(x-y-1\right)4\)
\(1,x^2y-x^3-9y+9x=x^2\left(y-x\right)-9\left(y-x\right).\)
\(\left(y-x\right)\left(x^2-9\right)=\left(y-x\right)\left(x-3\right)\left(x+3\right)\)
\(2,9x^2-1=\left(3x\right)^2-1^2=\left(3x+1\right)\left(3x-1\right)\)
\(3,\left(x-y\right)4-4=4\left(x-y-1\right)\)
\(4,\)\(9\left(x-y\right)^2=3^2\left(x-y\right)^2=\left(3x-3y\right)^2\)
\(5,3x^2-6ab+3b^2-12c^2???\)
\(6,x^2-25+y^2+2xy=\left(x+y\right)^2-25\)
\(=\left(x+y-5\right)\left(x+y+5\right)\)
1. x3 + 8 = (x + 2 )(x2 - x + 1)
2. 27 - 8y3 = ( 3 - 2y ) ( 9 + 6y + 4y2 )
3. y6 + 1 = (y2)3 + 1 = ( y2 + 1) ( y4 - y2 +1 )
4.64x3 - \(\dfrac{1}{8}\)y3 = ( 4x - \(\dfrac{1}{2}\)y ) ( 16x2 + 2xy + \(\dfrac{1}{4}\)y2)
5. 125x6 - 27y9 = (5x2)3 - (3y3)3
= ( 5x2 - 3y3)(25x4 +15x2y3 + 9y6)
a) \(x^3-x^2-5x+125\)
\(=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)\)
\(=\left(x+5\right)\left(x^2-6x+25\right)\)
b) \(5x^2-5xy-3x+3y\)
\(=5x\left(x-y\right)-3\left(x-y\right)\)
\(=\left(x-y\right)\left(5x-3\right)\)
c) \(x^2-2x-4y^2+1\)
\(=\left(x-1\right)^2-4y^2\)
\(=\left(x-2y-1\right)\left(x+2y-1\right)\)
a) 3x2 - 7x + 2
= 3x2 - 6x - x + 2
= (3x2 - 6x) - (x - 2)
= 3x (x - 2) - (x - 2)
= (3x - 1) (x - 2)
a) x4 - y4
= (x2)2 - (y2)2
= (x2 - y2)(x2 + y2)
= (x - y)(x + y)(x2 + y2)
a.\(x^4-y^4=\left(x^2\right)^2-\left(y^2\right)^2=\left(x^2-y^2\right)\left(x^2+y^2\right)=\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\)g,\(27x^3-0.001=27x^3-0=27x^3\)
\(x^3+1-x^2-x\)
\(=\left(x+1\right)\left(x^2-x+1\right)-x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-2x+1\right)\)
\(=\left(x+1\right)\left(x-1\right)^2\)
\(x+y-x^3-y^3\)
\(=\left(x+y\right)-\left(x+y\right)\left(x^2-xy+y^2\right)\)
\(=\left(x+y\right)\left(1-x^2+xy-y^2\right)\)
\(x^4-y^4\)
\(=\left(x^2\right)^2-\left(y^2\right)^2\)
\(=\left(x^2+y^2\right)\left(x^2-y^2\right)\)
\(125x^3-1\)
\(=\left(5x\right)^3-1^3\)
\(=\left(5x-1\right)\left(25x^2+5x+1\right)\)