1:

a: \(\left(2x-5\right)^2-4x\left(x+3\right)\)

\(=4x^2-20x+25-4x^2-12x\)

=-32x+25

b: \(\left(x-2\right)^3-6\left(x+4\right)\left(x-4\right)-\left(x-2\right)\left(x^2+2x+4\right)\)

\(=x^3-6x^2+12x-8-\left(x^3-8\right)-6\left(x^2-16\right)\)

\(=-6x^2+12x-6x^2+96=-12x^2+12x+96\)

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

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

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

\(=9+10x-15=10x-6\)

2: 

a: \(\left(2-3x\right)^2-5x\left(x-4\right)+4\left(x-1\right)\)

\(=9x^2-12x+4-5x^2+20x+4x-4\)

\(=4x^2+12x\)

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

\(=27-x^3+x^3-9x^2+27x-27\)

\(=-9x^2+27x\)

c: \(\left(x-4\right)^2\left(x+4\right)-\left(x-4\right)\left(x+4\right)^2+3\left(x^2-16\right)\)

\(=\left(x-4\right)\left(x+4\right)\left(x-4-x-4\right)+3\left(x^2-16\right)\)

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

\(=-5\left(x^2-16\right)=-5x^2+80\)

\(\left(x-2\right)\left(x^2+2x+4\right)+3x-4=\left(x+2\right)\left(x^2-2x+4\right)-x+1\)

\(\Rightarrow\left(x^3-8\right)+3x-4=\left(x^3+8\right)-x+1\)

\(\Rightarrow x^3-8+3x-4=x^3+8-x+1\)

\(\Rightarrow x^3-x^3+3x+x=8+8+4+1\)

\(\Rightarrow4x=21\)

\(\Rightarrow x=\dfrac{21}{5}\)

Nhân vô là ra ahah

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

\(b,=\dfrac{x^4-3x^2-x^2+3}{x^4-x^2+7x^2-7}=\dfrac{\left(x^2-3\right)\left(x^2-1\right)}{\left(x^2+7\right)\left(x^2-1\right)}=\dfrac{x^2-3}{x^2+7}\\ c,=\dfrac{\left(x^3-1\right)\left(x+1\right)}{x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)}\\ =\dfrac{\left(x-1\right)\left(x^2+x+1\right)\left(x+1\right)}{\left(x^2+1\right)\left(x^2+x+1\right)}=\dfrac{x^2-1}{x^2+1}\)

1a) -3x²(2x³ - 2x + 1/3) = -6x⁵ + 6x³ - x²

b) (x⁴ + 2x³ - 2/3).(-3x⁴) = -3x⁸ - 6x⁷ + 2x⁴

c) (x + 3)(x - 4) = x² - 4x + 3x - 12 = x² - x - 12

d)(x - 4)(x² + 4x + 16) = (x - 4)(x² + 4x + 4²) = x³ - 64

e) 4(x - 1/2)(x + 1/2)(4x² + 1) =4(x² - 1/4)(4x²  + 1) = 4(4x⁴ + x² - x² - 1/4) = 4(4x⁴ - 1/4) = 16x⁴ - 1

B2. a) (2 - x)(x² + 2x + 4) + x(x - 3)(x + 4) - x² + 24 = 0

=> 8 - x³ + x(x² + 4x - 3x - 12) - x² + 24 = 0

=> 8 - x³ + x³ + x² - 12x - x² + 24 = 0

=> -12x + 32 = 0

=> -12x = -32

=> x = -32 : (-12) = 8/3

b) (x/2 + 3)(5 - 6x) + (12x - 2)(x/4 + 3) = 0

=> 5x/2 - 3x² + 15 - 18x + 3x² + 36x - x/2 - 6 = 0

=> 20x + 9 = 0

=> 20x = -9

=> x = -9/20

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