cứu em ạa
a: \(A=x^3-x^2y+\dfrac{xy^2}{3}-\dfrac{y^3}{27}\)
\(=x^3-3\cdot x^2\cdot\dfrac{1}{3}y+3\cdot x\cdot\left(\dfrac{1}{3}y\right)^2-\left(\dfrac{1}{3}y\right)^3\)
\(=\left(x-\dfrac{1}{3}y\right)^3\)
Thay x=-1;y=27 vào A, ta được:
\(A=\left(-1-\dfrac{1}{3}\cdot27\right)^3=\left(-1-9\right)^3\)
\(=\left(-10\right)^3\)
=-1000
b: a chia 6 dư 5 nên a=6k+5
\(a^3-5=\left(6k+5\right)^3-5\)
\(=\left(6k+5-5\right)\left[\left(6k+5\right)^2+5\left(6k+5\right)+5^2\right]\)
\(=6k\cdot\left[\left(6k+5\right)^2+5\left(6k+5\right)+25\right]⋮6\)
=>\(a^3\) chia 6 dư 5
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