Giải bài 1 trang 16

Đề bài

Thực hiện phép tính:

a) $\left(-xy\right)\left(-2x^{2}y+3xy-7x\right)$                               

b) $\left(\frac{1}{6}{x}^2{y}^2\right)\left(-0,3x^{2}y-0,4xy+1\right)$

c) $\left(x+y\right)\left(x^2+2xy+y^2\right)$                                    

d) $\left(x-y\right)\left(x^2-2xy+y^2\right)$

Lời giải chi tiết

a)

$\begin{array}{c}\left(-xy\right)\left(-2x^{2}y+3xy-7x\right)\\ =\left(-xy\right).\left(-2x^{2}y\right)+\left(-xy\right)\left(3xy\right)+\left(-xy\right).\left(-7x\right)\\ =2x^3{y}^2-3x^2{y}^2+7x^{2}y\end{array}$

b)

$\begin{array}{c}\left(\frac{1}{6}{x}^2{y}^2\right)\left(-0,3x^{2}y-0,4xy+1\right)\\ =\left(\frac{1}{6}{x}^2{y}^2\right).\left(-0,3x^{2}y\right)+\left(\frac{1}{6}{x}^2{y}^2\right).\left(-0,4xy\right)+\left(\frac{1}{6}{x}^2{y}^2\right).1\\ =-\frac{1}{20}{x}^4{y}^3-\frac{1}{15}{x}^3{y}^3+\frac{1}{6}{x}^2{y}^2\end{array}$

c)

$\begin{array}{c}\left(x+y\right)\left(x^2+2xy+y^2\right)\\ =x.x^2+x.2xy+x.y^2+y.x^2+y.2xy+y.y^2\\ =x^3+2x^{2}y+x{y}^2+x^{2}y+2x{y}^2+y^3\\ =x^3+3x^{2}y+3x{y}^2+y^3\end{array}$

d)

$\begin{array}{c}\left(x-y\right)\left(x^2-2xy+y^2\right)\\ =x.x^2+x.\left(-2xy\right)+x.y^2+\left(-y\right).x^2+\left(-y\right).\left(-2xy\right)+\left(-y\right).y^2\\ =x^3-2x^{2}y+x{y}^2-x^{2}y+2x{y}^2-y^3\\ =x^3-3x^{2}y+3x{y}^2-y^3\end{array}$