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(x-1)(x-2)(x+2)-(x-3)\(^3\)
=(x-1)(x\(^2\)-4)-(x-3)\(^3\)
(xy-1)(xy-2)-(xy-2)\(^2\)
=(xy-2)(xy-1-xy+2)
=xy-2
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\(a,=\left[\left(x+2\right)-\left(x-3\right)\right]^2=\left(x+2-x+3\right)^2=5^2=25\)
\(b=x^2-5\)
\(c=\left(x+y-x+y\right)\left(x+y+x-y\right)=2y.2x=4xy\)
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\(D=\dfrac{5}{2x^2+6x}-\dfrac{4-3x^2}{x^2-9}-3\) (đk:\(x\ne3;x\ne-3\))
\(=\dfrac{5}{2x\left(x+3\right)}-\dfrac{4-3x^2}{\left(x-3\right)\left(x+3\right)}-3\)
\(=\dfrac{5\left(x-3\right)}{2x\left(x-3\right)\left(x+3\right)}-\dfrac{\left(4-3x^2\right).2x}{2x\left(x-3\right)\left(x+3\right)}-\dfrac{3.2x\left(x-3\right)\left(x+3\right)}{2x\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{5x-15-8x+6x^3-6x\left(x^2-9\right)}{2x\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{51x-15}{2x\left(x-3\right)\left(x+3\right)}\)
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Ta có: \(\left(x+5\right)\left(x^2-5x+25\right)-\left(x+3\right)^3+\left(x-2\right)\left(x^2+2x+4\right)-\left(x-1\right)^3\)
\(=x^3+125-x^3-9x^2-27x-27+x^3-8-x^3+3x^2-3x+1\)
\(=-6x^2-30x+91\)
\(x^3+15x^2+75x+125-x^3-125\)
\(15x^2+75x\)
\(15x\left(x+5\right)\)