(2x + 1)2 + (3x – 1)2 + 2(2x + 1)(3x – 1)

= (2x + 1)2 + 2.(2x + 1)(3x – 1) + (3x – 1)2

= [(2x + 1) + (3x – 1)]2

= (2x + 1 + 3x – 1)2

= (5x)2

= 25x2

\(A=2x^2\left(3x+4\right)\left(3x-4\right)-\dfrac{9}{2}\left(2x^2+1\right)\left(2x^2-1\right)\)

\(=2x^2\left(9x^2-16\right)-\dfrac{9}{2}\left(4x^4-1\right)\)

\(18x^4-32x^2-18x^4+\dfrac{9}{2}\\ =-32x^2+\dfrac{9}{2}\)

Ta có: \(A=2x^2\left(3x+4\right)\left(3x-4\right)-\dfrac{9}{2}\left(2x^2+1\right)\left(2x^2-1\right)\)

\(=2x^2\left(9x^2-16\right)-\dfrac{9}{2}\left(4x^4-1\right)\)

\(=18x^4-36x^2-18x^4+\dfrac{9}{2}\)

\(=-36x^2+\dfrac{9}{2}\)

`-3x(2x+1)+(2x-1)(3x+2)`

`=-6x^2-3x+6x^2+4x-3x-2`

`=(6x^2-6x^2)+(4x-3x-3x)-2`

`=-2x-2`

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

= \(-2x-2\)

Ta có: \(-3x\left(2x+1\right)+\left(2x-1\right)\left(3x+2\right)\)

\(=-6x^2-3x+6x^2+4x-3x-2\)

\(=-2x-2\)

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

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

\(=-2x-2\)

 (2x+1)*(2x-1)-(3x+1)²-(3x-2)*(5-2x)

=4x²-1-(9x²+6x+1)-(15x-6x²-10+4x)

=4x²-1-9x²-6x-1-15x+6x²+10-4x

=x²-25x+8

a) Ta có: \(\dfrac{2x^2-2x}{x-1}\)

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

=2x

b) Ta có: \(\dfrac{x^2+2x+1}{3x^2+3x}\)

\(=\dfrac{\left(x+1\right)^2}{3x\left(x+1\right)}\)

\(=\dfrac{x+1}{3x}\)

c) Ta có: \(\dfrac{x}{3x-3}+\dfrac{1}{x^2-1}\)

\(=\dfrac{x}{3\left(x-1\right)}+\dfrac{1}{\left(x-1\right)\left(x+1\right)}\)

\(=\dfrac{x+1+3}{3\left(x-1\right)\left(x+1\right)}\)

\(=\dfrac{x+4}{3x^2-3}\)

a, \(\dfrac{2x^2-2x}{x-1}=\dfrac{2x\left(x-1\right)}{x-1}=2x\) ( đk : \(x\ne1\) )

b,\(\dfrac{x^2+2x+1}{3x^2+3x}=\dfrac{\left(x+1\right)^2}{3x\left(x+1\right)}=\dfrac{x+1}{3x}\) ( đk : \(x\ne-1\) )

c

=

\(\left(3x+1\right)^2+2\left(3x+1\right)\left(2x-1\right)+\left(2x-1\right)^2=\left(3x+1+2x-1\right)^2=25x^2\)

1: \(=6x^2+2x-15x-5-x^2+6x-9+4x^2+20x+25-27x^3-27x^2-9x-1\)

=-27x^3-18x^2+4x+10

2: =4x^2-1-6x^2-9x+4x+6-x^3+3x^2-3x+1+8x^3+36x^2+54x+27

=7x^3+37x^2+46x+33

5:

\(=25x^2-1-x^3-27-4x^2-16x-16-9x^2+24x-16+\left(2x-5\right)^3\)

\(=8x^3-60x^2+150-125+12x^2-x^3+8x-60\)

=7x^3-48x^2+8x-35

a: \(=\dfrac{\left(x-1\right)\left(x+1\right)}{\left(x+1\right)^2}=\dfrac{x-1}{x+1}\)

b: \(=\dfrac{\left(x-1\right)\cdot\left(x+1\right)}{\left(x-1\right)^2}=\dfrac{x+1}{x-1}\)

c: \(=\dfrac{3x+2-3x+2+3x-6}{\left(3x-2\right)\left(3x+2\right)}=\dfrac{3x-2}{\left(3x-2\right)\left(3x+2\right)}=\dfrac{1}{3x+2}\)

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