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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: \(\left(x-4\right)^2\left(x+4\right)-\left(x-4\right)\left(x+4\right)^2+3\left(x^2-16\right)\)
\(=\left(x-4\right)\left(x+4\right)\left(x-4-x-4\right)+3\left(x^2-16\right)\)
\(=\left(x^2-16\right)\left(-8\right)+3\left(x^2-16\right)\)
\(=-5\left(x^2-16\right)=-5x^2+80\)
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: \(P=\dfrac{x^2-2x-3+3-2x}{x-4}=\dfrac{x^2-4x}{x-4}=x\)
a: \(=\dfrac{2\left(x+2\right)\left(x-1\right)}{x+2}=2x-2\)
b: \(=\dfrac{2x^3+x^2-6x^2-3x+2x+1}{2x+1}=x^2-3x+1\)
c: \(=\dfrac{x^3+2x^2-2x^2-4x+2x+4}{x+2}=x^2-2x+2\)
d: \(=\dfrac{x^2\left(x-3\right)}{x-3}=x^2\)
b: =>4x^2+8x-8x^2+5x-10=0
=>-4x^2+13x-10=0
=>x=2 hoặc x=5/4
c: =>2x^2-5x+6x-15=2x^2+8x
=>x-15=8x
=>-7x=15
=>x=-15/7
d: =>3x^2+15x-2x-10-3x^2-12x=5
=>x-10=5
=>x=15
e: =>x^2-3x+2x^2+2x=3x^2-12
=>-x=-12
=>x=12
a) (2x + 1)(1 - 2x) + (1 - 2x)2 = 18
= ( 1 - 2x) \(\left[\left(2x+1+1-2x\right)\right]\) = 18
= 2(1 - 2x) - 18 = 0
= 2 - 4x - 18 = 0
= -16 - 4x = 0
= -4x = 16
= x = \(\dfrac{16}{-4}=-4\)
b) 2(x + 1)2 -(x - 3)(x + 3) - (x - 4)2 = 0
= 2 (x2 + 2x + 1) - (x2 - 9) - (x2 - 8x + 16) = 0
= 2x2 + 4x + 2 - x2 + 9 - x2 + 8x - 16 = 0
= 12x - 5 = 0
= 12x = 5
= x = \(\dfrac{5}{12}\)
c) (x - 5)2 - x(x - 4) = 9
= x2 - 10x + 25 - x2 + 4x - 9 = 0
= -6x + 16 = 0
= -6x = -16
= x = \(\dfrac{-16}{-6}=\dfrac{8}{3}\)
d) (x - 5)2 + (x - 4)(1 - x)
= x2 - 10x + 25 + 5x - x2 - 4 = 0
= -5x + 21 = 0
= -5x = -21
= x = \(\dfrac{-21}{-5}=\dfrac{21}{5}\)
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