a)

\(\left(\right. x - 2 y \left.\right) \left(\right. 3 x y + 6 x^{2} + x \left.\right)\)

Nhân phân phối:

\(= x \left(\right. 3 x y + 6 x^{2} + x \left.\right) - 2 y \left(\right. 3 x y + 6 x^{2} + x \left.\right)\)\(= \left(\right. 3 x^{2} y + 6 x^{3} + x^{2} \left.\right) - \left(\right. 6 x y^{2} + 12 x^{2} y + 2 x y \left.\right)\)

Gộp hạng tử:

\(= 6 x^{3} + x^{2} - 9 x^{2} y - 6 x y^{2} - 2 x y\)

\(\boxed{6 x^{3} + x^{2} - 9 x^{2} y - 6 x y^{2} - 2 x y}\)

b)

\(\left(\right. 18 x^{4} y^{3} - 24 x^{3} y^{4} + 12 x^{3} y^{3} \left.\right) : \left(\right. - 6 x^{2} y^{3} \left.\right)\)

Chia từng hạng tử:

\(= \frac{18 x^{4} y^{3}}{- 6 x^{2} y^{3}} + \frac{- 24 x^{3} y^{4}}{- 6 x^{2} y^{3}} + \frac{12 x^{3} y^{3}}{- 6 x^{2} y^{3}}\)

Tính:

• \(= - 3 x^{2}\)
• \(= + 4 x y\)
• \(= - 2 x\)

\(\boxed{- 3 x^{2} + 4 x y - 2 x}\)

P=2x2y−3x+8y2−1

a)

• Các hạng tử: \(2 x^{2} y ; \&\text{nbsp}; - 3 x ; \&\text{nbsp}; 8 y^{2} ; \&\text{nbsp}; - 1\)
• Bậc của đa thức: 3 (vì \(2 x^{2} y\) có bậc \(2 + 1 = 3\) là cao nhất)

b) Thay \(x = - 1 , \&\text{nbsp}; y = \frac{1}{2}\)

\(P = 2 \left(\right. - 1 \left.\right)^{2} \cdot \frac{1}{2} - 3 \left(\right. - 1 \left.\right) + 8 \left(\left(\right. \frac{1}{2} \left.\right)\right)^{2} - 1\)

Tính:

• \(2 \cdot 1 \cdot \frac{1}{2} = 1\)
• \(- 3 \left(\right. - 1 \left.\right) = 3\)
• \(8 \cdot \frac{1}{4} = 2\)

\(P = 1 + 3 + 2 - 1 = 5\)

   \(P = 5\)