(8x⁴y³+24x³y²–2x²y²):(4x²y²)
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\(x\left(y-1\right)-y\left(y-1\right)\)
\(=\left(y-1\right)\left(x-y\right)\)
_________________
\(5x\left(x-2\right)-x+2\)
\(=5x\left(x-2\right)-\left(x-2\right)\)
\(=\left(x-2\right)\left(5x-1\right)\)
_________________
\(5x\left(x+1\right)-8x-8\)
\(=5x\left(x+1\right)-\left(8x+8\right)\)
\(=5x\left(x+1\right)-8\left(x+1\right)\)
\(=\left(x+1\right)\left(5x-8\right)\)
a: \(=\dfrac{2xy\left(2x^2y-4x+5\right)}{2xy}=2x^2y-4x+5\)
b: \(=\dfrac{x^2y\left(7x^2y-2y-5x^2y^3\right)}{3x^2y}=\dfrac{7}{3}x^2y-\dfrac{2}{3}y-\dfrac{5}{3}x^2y^3\)
1) a) \(x^3-2x^2y+xy^2-25x=x\left(x^2-2xy+y^2-25\right)\)
\(=x\left[\left(x-y\right)^2-5^2\right]=x\left(x-y-5\right)\left(x-y+5\right)\)
b)\(x^2-y^2-2x-2y=\left(x^2-2x+1\right)-\left(y^2+2y+1\right)=\left(x-1\right)^2-\left(y+1\right)^2\)
\(=\left(x-1-y-1\right)\left(x-y+y+1\right)=\left(x-y-2\right)\left(x+1\right)\)
6, x mũ 4 - 4x mũ 3 - 8x mũ 2 + 8x =x (x+2) (x^2-6x+4)
8, x mũ 4 + 2x mũ 3 + x mũ 2 - y mũ 2 = -(y-x^2-x) (y+x^2+x)
10, 4x mũ 2 ( x + y ) -x - y = (2x-1) (2x+1) (y+x)
Bài 4:
\(x^3-2x^2+x=x\left(x-1\right)^2\)
\(5\left(x-y\right)-y\left(x-y\right)=\left(x-y\right)\left(5-y\right)\)
\(x^2-12x+36=\left(x-6\right)^2\)
1 ) ( 2x - 1 ) ( 8x + 12 ) + x2( 2x - 1 ) + ( 1 - 2x ).( 2x - 3 )
= ( 2x - 1 ) . ( 8x + 12 ) + x2 ( 2x - 1 ) - ( 2x - 1 ) . ( 2x - 3 )
= ( 2x - 1 ) . ( 8x + 12 + x2 - 2x + 3 )
= ( 2x - 1 ) . ( x2 + 6x + 15 )
2 ) 3x ( x - y ) - 2y ( y - x ) - 4x + 4y
= 3x ( x - y ) + 2y ( x - y ) - 4. ( x - y )
= ( x - y ) ( 3x + 2y - 4 )
\(\dfrac{8x^4y^3+24x^3y^2-2x^2y^2}{4x^2y^2}\)
\(=\dfrac{8x^4y^3}{4x^2y^2}+\dfrac{24x^3y^2}{4x^2y^2}-\dfrac{2x^2y^2}{4x^2y^2}\)
\(=2x^2y+6x-\dfrac{1}{2}\)