Question

Rút gọn biểu thức:

a) Q = \(\left(3x^2-5xy-4y^2\right).\left(2x^2+y^2\right)+\left(2x^4y^2+x^3y^3+x^2y^4\right):\left(\dfrac{1}{5}xy\right)\)

b) P = \(\left(x-3\right)\left(x^2+3x+9\right)+\left(2x-1\right)^3-x\left(3x-1\right)\left(3x+1\right)+3\left(2x+3\right)^2\)

Answer 1

a: \(Q=\left(3x^2-5xy-4y^2\right)\cdot\left(2x^2+y^2\right)+\left(2x^4y^2+x^3y^3+x^2y^4\right):\left(\dfrac{1}{5}xy\right)\)

\(=6x^4+3x^2y^2-10x^3y-5xy^3-8x^2y^2-4y^4+\dfrac{2x^4y^2}{\dfrac{1}{5}xy}+\dfrac{x^3y^3}{\dfrac{1}{5}xy}+\dfrac{x^2y^4}{\dfrac{1}{5}xy}\)

\(=6x^4-5x^2y^2-10x^3y-5xy^3-4y^4+10x^3y+5x^2y^2+5xy^3\)

\(=6x^4-4y^4\)

b: \(P=\left(x-3\right)\left(x^2+3x+9\right)+\left(2x-1\right)^3-x\left(3x-1\right)\left(3x+1\right)+3\left(2x+3\right)^2\)

\(=x^3-27+8x^3-12x^2+6x-1-x\left(9x^2-1\right)+3\left(4x^2+12x+9\right)\)

\(=9x^3-12x^2+6x-28-9x^3+x+3\left(4x^2+12x+9\right)\)

\(=-12x^2+7x-28+12x^2+36x+27\)

=43x-1