Bài 8 trang 8 SGK Toán lớp 8 Tập 1

\(a)\ (x^2y^2-\frac{1}{2xy}+2y)(x-2y)\)

\(\begin{array}{l} =x^{2} y^{2} \cdot x+x^{2} y^{2}(-2 x)+(x y) \cdot x+(-x x)(-2 y)+2 x \cdot x+2 y(-2 y) \\ =x^{3} y^{2}-2 x^{2} y^{3}-x^{2} y+x y^{2}+2 x y-4 y^{2} \end{array}\)

\(\begin{aligned} &\text { b) }\left(x^{2}-x y+y^{2}\right)(x+y)=x^{2} \cdot x+x^{2} \cdot y+(-x y) \cdot x+(-x y) \cdot y+y^{2} \cdot x+y 2 \cdot y\\ &=x^{3}+x^{2} \cdot y-x^{2} \cdot y-x y^{2}+x y^{2}+y^{3}\\ &=x^{3}+y^{3} \end{aligned}\)

\(a)\ (x^2y^2-\frac{1}{2xy}+2y)(x-2y)\)

\(\begin{array}{l} =x^{2} y^{2} \cdot x+x^{2} y^{2}(-2 x)+(x y) \cdot x+(-x x)(-2 y)+2 x \cdot x+2 y(-2 y) \\ =x^{3} y^{2}-2 x^{2} y^{3}-x^{2} y+x y^{2}+2 x y-4 y^{2} \end{array}\)

\(\begin{aligned} &\text { b) }\left(x^{2}-x y+y^{2}\right)(x+y)=x^{2} \cdot x+x^{2} \cdot y+(-x y) \cdot x+(-x y) \cdot y+y^{2} \cdot x+y 2 \cdot y\\ &=x^{3}+x^{2} \cdot y-x^{2} \cdot y-x y^{2}+x y^{2}+y^{3}\\ &=x^{3}+y^{3} \end{aligned}\)

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