Question

Rút gọn và thực hiện biểu thức

a) x\(^2\) .(x - y\(^2\)) - xy. (1 - yx) - x\(^3\)

b) x. (x + 3y + 1) - 2y. (x - 1)

c) (-xy\(^2\))\(^2\) . (x\(^2\) - 2x +1)

d) (x + 2y). (x\(^2\) - 2y + 4z)

e) \(\dfrac{27}{15}\)x\(^3\)yz\(^5\) : \(\dfrac{9}{5}\)xz\(^2\)

Answer 1

a: \(x^2\left(x-y^2\right)-xy\left(1-xy\right)-x^3\)

\(=x^3-x^2y^2-xy+x^2y^2-x^3\)

=-xy

b: \(x\left(x+3y+1\right)-2y\left(x-1\right)\)

\(=x^2+3xy+x-2xy+2y\)

\(=x^2+xy+x+2y\)

c: \(\left(-xy^2\right)^2\left(x^2-2x+1\right)\)

\(=x^2y^4\cdot\left(x^2-2x+1\right)\)

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

d: \(\left(x+2y\right)\left(x^2-2y+4z\right)\)

\(=x^3-2xy+4xz+2x^2y-4y^2+4yz\)

e: \(\dfrac{27}{15}x^3yz^5:\dfrac{9}{5}xz^2\)

\(=\left(\dfrac{27}{15}:\dfrac{9}{5}\right)\cdot\dfrac{x^3}{x}\cdot\dfrac{yz^5}{z^2}\)

\(=x^2yz^3\)