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\(a,\left(5x-2y\right)\left(x^2-xy+1\right)=5x^3-5x^2y+5x-2x^2y-2xy^2-2y=5x^3-7x^2y-2xy^2+5x-2y\)\(b\left(x-1\right)\left(x+1\right)\left(x-2\right)=\left(x^2-1\right)\left(x+2\right)=x^3+2x^2-x-2\)\(c,\dfrac{1}{2}x^2y^2\left(2x+y\right)\left(2x-y\right)=\dfrac{1}{2}x^2y^2\left(4x^2-y^2\right)=2x^4y^2-\dfrac{1}{2}x^2y^4\)
a) biết chết liền
b) \(\left(x^2-xy+y^2\right)\left(x+y\right)=x^3+y^3\)
a) (x2 – 2x + 3) (1212x – 5)
= 1212x3 - 5x2 - x2 +10x + 3232x – 15
= 1212x3 – 6x2 + 232232x -15
b) (x2 – 2xy + y2)(x – y)
= x3 - x2 y - 2x2 y + 2xy2 +xy2- y3
= x3 - 3x2 y + 3xy2 - y3
a) (x2 – 2x + 3) ( 1/2x – 5) = \(\dfrac{1}{2}\)x3 – 5x2 – x2 + 10x +\(\dfrac{3}{2}\)x - 15
= \(\dfrac{1}{2}\)x3 – 6x2 + \(\dfrac{23}{2}\) x – 15.
b) (x2 – 2xy + y2)( x – y) = x3 – x2y – 2x2y + xy2 – y3 = x3 – 3x2y + 3xy2 – y3
a) (x2 + 2xy + y2) : (x + y) = (x + y)2 : (x + y) = x + y.
b) (125x3 + 1) : (5x + 1) = [(5x)3 + 1] : (5x + 1)
= (5x)2 – 5x + 1 = 25x2 – 5x + 1.
c) (x2 – 2xy + y2) : (y – x) = (x – y)2 : [-(x – y)] = - (x – y) = y – x
Hoặc (x2 – 2xy + y2) : (y – x) = (y2 – 2xy + x2) : (y – x)
= (y – x)2 : (y – x) = y - x.
Bài giải:
a) (x2 + 2xy + y2) : (x + y) = (x + y)2 : (x + y) = x + y.
b) (125x3 + 1) : (5x + 1) = [(5x)3 + 1] : (5x + 1)
= (5x)2 – 5x + 1 = 25x2 – 5x + 1.
c) (x2 – 2xy + y2) : (y – x) = (x – y)2 : [-(x – y)] = - (x – y) = y – x
Hoặc (x2 – 2xy + y2) : (y – x) = (y2 – 2xy + x2) : (y – x)
= (y – x)2 : (y – x) = y - x.
a) ĐKXĐ: \(x;y\ne0,x\ne\frac{y}{2},y\ne\frac{x}{2}\)
\(\frac{y}{2x^2-xy}+\frac{4x}{y^2-2xy}=\frac{y}{x\left(2x-y\right)}-\frac{4x}{y\left(2x-y\right)}\)\(=\frac{y^2-4x^2}{xy\left(2x-y\right)}=\frac{\left(y-2x\right)\left(y+2x\right)}{xy\left(2x-y\right)}\)
\(=\frac{-\left(y+2x\right)}{xy}\)
b) ĐKXĐ: \(x\ne2;x\ne-2\)
\(\frac{1}{x+2}+\frac{3}{x^2-4}+\frac{x-14}{\left(x^2+4x+4\right)\left(x-2\right)}\)\(=\frac{1}{x+2}+\frac{3}{\left(x-2\right)\left(x+2\right)}+\frac{x-14}{\left(x+2\right)^2\left(x-2\right)}\)
\(=\frac{\left(x-2\right)\left(x+2\right)+3\left(x+2\right)+x-14}{\left(x+2\right)^2\left(x-2\right)}\)\(=\frac{x^2-4+3x+6+x-14}{\left(x+2\right)^2\left(x-2\right)}\)\(=\frac{x^2+4x-12}{\left(x+2\right)^2\left(x-2\right)}=\frac{\left(x^2+4x+4\right)-16}{\left(x+2\right)^2\left(x-2\right)}\)\(=\frac{\left(x+2\right)^2-16}{\left(x+2\right)^2\left(x-2\right)}=\frac{\left(x+2-4\right)\left(x+2+4\right)}{\left(x+2\right)^2\left(x-2\right)}\)\(=\frac{\left(x-2\right)\left(x+6\right)}{\left(x+2\right)^2\left(x-2\right)}=\frac{x+6}{\left(x+2\right)^2}\)
câu b ko ghi lại đề bài
\(\left(x-1\right)\left(x+2\right)\)
\(\Leftrightarrow1.\left[\left(x-1\right)+\left(x+2\right)\right]\)
\(=1.\left(2.x+1\right)\)
\(=2x+1\)