\(D=\left(2x+1\right)^2-\left(2x-3\right)^2+6x\)

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

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

\(D=-2x-8\)

_______________________

\(E=\left(x-4\right)^2-x\left(x+2\right)-2x+3\)

\(E=\left(x^2-8x+16\right)-\left(x^2+2x\right)-2x+3\)

\(E=\left(x^2-x^2\right)-\left(8x+2x+2x\right)+\left(16+3\right)\)

\(E=-12x+19\)

\(D=\left(2x+1\right)^2-\left(2x-3\right)^2+6x\)

\(D=\left[\left(2x\right)^2+2.2x.1+1^2\right]-\left[\left(2x\right)^2-2.2x.3+3^2\right]+6x\)

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

\(D=4x^2+4x+1-4x^2+12x-9+6x\)

\(D=22x-8\)

___________

\(E=\left(x-4\right)^2-x\left(x+2\right)-2x+3\)

\(E=\left(x^2-2.x.4+4^2\right)-\left(x^2+2x\right)-2x+3\)

\(E=x^2-8x+16-x^2-2x-2x+3\)

\(E=-12x+19\)

a) Rút gọn biểu thức D = (2x + 1)2 - (2x - 3)2 + 6x:

Bắt đầu bằng việc mở ngoặc:
D = (4x^2 + 4x + 1) - (4x^2 - 12x + 9) + 6x

Tiếp theo, kết hợp các thành phần tương tự:
D = 4x^2 + 4x + 1 - 4x^2 + 12x - 9 + 6x

Tiếp tục đơn giản hóa:
D = 4x^2 - 4x^2 + 4x + 12x + 6x + 1 - 9

Kết quả cuối cùng:
D = 22x - 8

b) Rút gọn biểu thức E = (x - 4)2 - x(x + 2) - 2x + 3:

Bắt đầu bằng việc mở ngoặc:
E = (x^2 - 8x + 16) - (x^2 + 2x) - 2x + 3

Tiếp theo, kết hợp các thành phần tương tự:
E = x^2 - 8x + 16 - x^2 - 2x - 2x + 3

Tiếp tục đơn giản hóa:
E = x^2 - x^2 - 8x - 2x - 2x + 16 + 3

Kết quả cuối cùng:
E = -12x + 19

\(D=\dfrac{x+1-x+1+4x+2}{\left(x-1\right)\left(x+1\right)}=\dfrac{4x+4}{\left(x-1\right)\left(x+1\right)}=\dfrac{4}{x-1}\)

D=4/2015

=>x-1=2015

=>x=2016

\(D=\dfrac{x+1-x+1+4x+2}{\left(x-1\right)\left(x+1\right)}=\dfrac{4}{x-1}\)

Khi x=9+4căn 5 thì \(D=\dfrac{4}{8+4\sqrt{5}}=\dfrac{1}{\sqrt{5}+2}=\sqrt{5}-2\)

\(D=xy^3\left(-4-\dfrac{1}{3}-2\right)+x^2y\left(6+1\right)-\dfrac{7}{2}x^3y=-\dfrac{19}{3}xy^3+7x^2y-\dfrac{7}{2}x^3y\)

\(\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(1+6x\right)\left(6x-1\right)\)

\(=\left(6x+1\right)^2-2\left(6x+1\right)\left(6x-1\right)+\left(6x-1\right)^2\)

\(=\left(6x+1-6x+1\right)^2\)

\(=4\)

\(x\left(2x^2-3\right)-x^2\left(5x+1\right)+x^2\)

\(=2x^3-3x-5x^3-x^2+x^2\)

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

\(=-3x^3-3x\)

\(3x\left(x-2\right)-5x\left(1-x\right)-8\left(x^2-3\right)\)

\(=3x^2-6x-5x+5x^2-8x^2+24\)

\(=\left(3x^2+5x^2-8x^2\right)-\left(6x+5x\right)+24\)

\(=-11x+24\)

\(N=x^3+3x^2+3x+1-x^3+3x^2-3x+1-6x^2=2\\ P=x^2-4xy-12y^2-x^2+4xy-4y^2=-16y^2\)

   (x+1)\(^3\)-(x-1)\(^3\)-6x\(^2\)

=x\(^3\)+3x\(^2\)+3x+1-x\(^3\)+3x\(^2\)-3x+1-6x\(^2\)

=2