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a) \(\dfrac{\left(x+y\right)^2}{2}\)
b)\(\dfrac{5a-5b}{2}\)
c)\(\left(x-2y\right)^2\)
\(A=4x^2-5xy+3y^2\\\Rightarrow 2A=2\cdot(4x^2-5xy+3y^2)\\\Rightarrow2A=8x^2-10xy+6y^2\\B=3x^2+2xy+y^2\\\Rightarrow3B=3\cdot(3x^2+2xy+y^2)\\\Rightarrow3B=9x^2+6xy+3y^2\\C=-x^2+3xy+2y^2\)
Khi đó: $2A-3B-C$
$=(8x^2-10xy+6y^2)-(9x^2+6xy+3y^2)-(-x^2+3xy+2y^2)$
$=8x^2-10xy+6y^2-9x^2-6xy-3y^2+x^2-3xy-2y^2$
$=(8x^2-9x^2+x^2)+(-10xy-6xy-3xy)+(6y^2-3y^2-2y^2)$
$=-19xy+y^2$
2A-3B-C
\(=2\left(4x^2-5xy+3y^2\right)-3\left(3x^2+2xy+y^2\right)+x^2-3xy-2y^2\)
\(=8x^2-10xy+6y^2-9x^2-6xy-3y^2+x^2-3xy-2y^2\)
\(=-19xy+y^2\)
e) = \(\dfrac{3}{2\left(x+3\right)}\) - \(\dfrac{x-6}{2x\left(x+3\right)}\)
= \(\dfrac{3x}{2x\left(x+3\right)}\) - \(\dfrac{x-6}{2x\left(x+3\right)}\) = \(\dfrac{3x-x+6}{2x\left(x+3\right)}\)
= \(\dfrac{2x-6}{2x\left(x+3\right)}\)
= \(\dfrac{2\left(x-3\right)}{2x\left(x+3\right)}\)
c) = \(\dfrac{2\left(a^3-b^3\right)}{3\left(a+b\right)}\) . \(\dfrac{6\left(a+b\right)}{a^2-2ab+b^2}\)
= \(\dfrac{-2\left(a+b\right)\left(a^2-2ab+b^2\right)}{3\left(a+b\right)}\) . \(\dfrac{6\left(a+b\right)}{a^2-2ab+b^2}\)
= \(\dfrac{-2\left(a+b\right)}{1}\) . \(\dfrac{2}{1}\) = -4 (a+b)
a: \(=\left[\dfrac{3xy\left(x-2x^2y\right)}{3xy}+6x^2y-x\right]^2:\dfrac{1}{2}x^2\)
\(=\left[x-2x^2y+6x^2y-x\right]^2:\dfrac{1}{2}x^2\)
\(=\dfrac{16x^4y^2}{0.5x^2}=32x^2y^2\)
b: \(=\dfrac{7\left(a-b\right)^5+5\left(a-b\right)^3}{\left(a-b\right)^2}=7\left(a-b\right)^3+5\left(a-b\right)\)
c: \(=\dfrac{7\left(a-3b\right)^3+\left(a-3b\right)}{2\left(a-3b\right)}=\dfrac{7\left(a-3b\right)^2+1}{2}\)