\(=27a^6-18a^4b^3+12a^2b^6-18a^4b^3+12a^2b^6-8b^9\)

\(=27a^6-36a^4b^3+24a^2b^6-8a^9\)

\(A=\left(x+y\right)^2+\left(y-x\right)^2-2\left(x-y\right)\left(x+y\right)\)

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

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

\(=\left(2y\right)^2\)Thay \(y=\frac{1}{2}\)ta được:
\(\left(2.\frac{1}{2}\right)^2\)

\(=1\)

Vậy \(A=1\)tại \(x=2019\)và \(y=\frac{1}{2}\)

A = (x + y)^2 + (y - x)^2 - 2(x - y)(x + y)

A = x^2 + 2xy + y^2 + x^2 - 2xy + y^2 - 2x^2 + 2y^2

A = (x^2 + x^2 - 2x^2) + (2xy - 2xy) + (y^2 + y^2 + 2y^2)

A = 4y^2 (1)

Thay x = 2019 và y = 1/2 vào (1), ta có:

(4.1/2)^2 = 4

a=1-2x

bạn có thể trình bày cụ thể hơn được ko

x²-8xy+15y² +2x-4y-3

= (x-4y)² - y² + (2x-8y) +4y -3

= (x-4y)² +2(x-4y) +1 - y²+4y-4

= (x-4y+1)² -(y-2)²  = (x-3y-1)(y-5y+3)

a) \(P=\left(\frac{1}{x-1}-\frac{x}{1-x^3}.\frac{x^2+x+1}{x+1}\right):\frac{2x+1}{x^2+2x+1}\)

\(=\left(\frac{1}{x-1}-\frac{x}{\left(1-x\right)\left(1+x+x^2\right)}.\frac{x^2+x+1}{x+1}\right).\frac{x^2+2x+1}{2x+1}\)

\(=\left(\frac{1}{x-1}-\frac{x}{\left(x-1\right)\left(x+1\right)}\right).\frac{x^2+2x+1}{2x+1}\)

\(=\left(\frac{x+1}{\left(x-1\right)\left(x+1\right)}-\frac{x}{\left(x-1\right)\left(x+1\right)}\right).\frac{x^2+2x+1}{2x+1}\)

\(=\frac{1}{\left(x-1\right)\left(x+1\right)}.\frac{\left(x+1\right)^2}{2x+1}\)

\(=\frac{x+1}{\left(x-1\right)\left(2x+1\right)}\)

b) \(Q=\frac{x^2+2x}{2x+10}+\frac{x-5}{x}+\frac{5x-5x}{2x\left(x+5\right)}\)

\(=\frac{x\left(x^2+2x\right)}{2x\left(x+5\right)}+\frac{2\left(x-5\right)\left(x+5\right)}{2x\left(x+5\right)}+\frac{50-5x}{2x\left(x+5\right)}\)

\(=\frac{x^3+2x^2+2\left(x^2-25\right)+50-5x}{2x\left(x+5\right)}\)

\(=\frac{x^3+2x^2+2x^2-50+50-5x}{2x\left(x+5\right)}\)

\(=\frac{x^3+4x^2-5x}{2x\left(x+5\right)}\)

\(=\frac{x^3-x^2+5x^2-5x}{2x\left(x+5\right)}\)

\(=\frac{x^2\left(x-1\right)+5x\left(x-1\right)}{2x\left(x+5\right)}\)

\(=\frac{\left(x-1\right)\left(x^2+5x\right)}{2x\left(x+5\right)}\)

\(=\frac{x\left(x-1\right)\left(x+5\right)}{2x\left(x+5\right)}\)

\(=\frac{x-1}{2}\)

a) \(P=\frac{2}{2x+3}+\frac{3}{2x+1}-\frac{6x+5}{\left(2x+3\right)\left(2x-3\right)}\)

\(=\frac{2\left(2x+1\right)\left(2x-3\right)}{\left(2x+3\right)\left(2x-3\right)\left(2x+1\right)}+\frac{3\left(2x+3\right)\left(2x-3\right)}{\left(2x+1\right)\left(2x+3\right)\left(2x-3\right)}-\frac{\left(6x+5\right)\left(2x+1\right)}{\left(2x+3\right)\left(2x-3\right)\left(2x+1\right)}\)

\(=\frac{\left(4x+2\right)\left(2x-3\right)+3\left(4x^2-9\right)-12x^2-16x-5}{\left(2x+3\right)\left(2x-3\right)\left(2x+1\right)}\)

\(=\frac{8x^2-8x-6+12x^2-27-12x^2-16x-5}{\left(2x+3\right)\left(2x-3\right)\left(2x+1\right)}\)

\(=\frac{8x^2-24x-38}{\left(2x+3\right)\left(2x-3\right)\left(2x+1\right)}\)

Check hộ mình xem nghi nghi sai sai

b) \(Q=\left(\frac{x+1}{2x-1}+\frac{3}{x^2-1}-\frac{x+3}{2x+2}\right).\frac{4x^2-4}{5}\)

\(=\left(\frac{x+1}{2x-1}+\frac{3}{\left(x-1\right)\left(x+1\right)}-\frac{x+3}{2\left(x+1\right)}\right).\frac{4x^2-4}{5}\)

\(=\left(\frac{2\left(x+1\right)\left(x-1\right)\left(x+1\right)}{2\left(2x-1\right)\left(x-1\right)\left(x+1\right)}+\frac{2.3\left(2x-1\right)}{2\left(x-1\right)\left(x+1\right)\left(2x-1\right)}-\frac{\left(x+3\right)\left(2x-1\right)\left(x-1\right)}{2\left(x+1\right)\left(2x-1\right)\left(x-1\right)}\right).\frac{4x^2-4}{5}\)

\(=\frac{2\left(x+1\right)\left(x^2-1\right)+12x-6-\left(2x^2+5x-3\right)\left(x-1\right)}{2\left(2x-1\right)\left(x+1\right)\left(x-1\right)}.\frac{4x^2-4}{5}\)

\(=\frac{2\left(x^3+x^2-x-1\right)+12x-6-2x^3-5x^2+3x+2x^2+5x-3}{2\left(2x-1\right)\left(x+1\right)\left(x-1\right)}.\frac{4x^2-4}{5}\)

\(=\frac{2x^3+2x^2-2x-2+20x-2x^3-3x^2-9}{2\left(2x-1\right)\left(x+1\right)\left(x-1\right)}.\frac{4x^2-4}{5}\)

\(=\frac{-x^2+18x-11}{2\left(2x-1\right)\left(x+1\right)\left(x-1\right)}.\frac{4\left(x-1\right)\left(x+1\right)}{5}\)

\(=\frac{-x^2+18x-11}{\left(2x-1\right)}.\frac{2}{5}\)

\(=\frac{-2x^2+36x-22}{5\left(2x-1\right)}\)

a) \(P=\frac{x}{2x-2}+\frac{x^2+1}{2-2x^2}\)

\(P=\frac{x}{2\left(x-1\right)}+\frac{x^2+1}{2\left(1-x^2\right)}\)

\(P=\frac{x}{2\left(x-1\right)}-\frac{x^2+1}{2\left(x^2-1\right)}\)

\(P=\frac{x}{2\left(x-1\right)}-\frac{x^2+1}{2\left(x-1\right)\left(x+1\right)}\)

\(P=\frac{x\left(x+1\right)-x^2-1}{2\left(x-1\right)\left(x+1\right)}\)

\(P=\frac{x^2+x-x^2-1}{2\left(x-1\right)\left(x+1\right)}\)

\(P=\frac{x-1}{2\left(x-1\right)\left(x+1\right)}=\frac{1}{2\left(x+1\right)}\)

b) \(Q=\frac{x^2+2x}{2x+10}+\frac{x-5}{x}+\frac{50-5x}{2x\left(x+5\right)}\)

\(Q=\frac{x\left(x+2\right)}{2\left(x+5\right)}+\frac{x-5}{x}+\frac{50-5x}{2x\left(x+5\right)}\)

\(Q=\frac{x^2\left(x+2\right)+2\left(x+5\right)\left(x-5\right)+50-5x}{2x\left(x+5\right)}\)

\(Q=\frac{x^3+2x^2+2\left(x^2-25\right)+50-5x}{2x\left(x+5\right)}\)

\(Q=\frac{x^3+2x^2+2x^2-50+50-5x}{2x\left(x+5\right)}\)

\(Q=\frac{x^3+4x^2-5x}{2x\left(x+5\right)}\)

\(Q=\frac{x\left(x^2+4x-5\right)}{2x\left(x+5\right)}=\frac{x^2+4x-5}{2\left(x+5\right)}\)