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1) (x - 5)^2 + (x + 3)^2 = 2(x - 4)(x + 4) - 5x + 7
<=> x^2 - 10x + 25 + x^2 + 6x + 9 = 2x^2 + 8x - 8x - 32 - 5x + 7
<=> 2x^2 - 4x + 34 = 2x^2 - 5x - 25
<=> -4x + 34 = -5x - 25
<=> x + 34 = -25
<=> x = -25 - 34
<=> x = - 59
2) (x + 3)(x - 2) - 2(x + 1)^2 = (x - 3)^2 - 2x^2 + 4x
<=> x^2 - 2x + 3x - 6 - 2x^2 - 4x - 2 = x^2 - 6x + 9 - 2x^2 + 4x
<=> -x^2 - 3x - 8 = -x^2 - 2x + 9
<=> -3x - 8 = -2x + 9
<=> -x - 8 = 9
<=> -x = 9 + 8
<=> x = -17
3) (x + 1)^3 - (x + 2)(x - 4) = (x - 2)(x^2 + 2x + 4) + 2x^2
<=> x^3 + 2x^3 + x + x^2 + 2x + 1 - x^2 + 4x - 2x + 8 = x^3 + 2x^2 + 4x - 2x^2 - 4x - 8 + 2x^2
<=> 2x^2 + 5x + 9 = 2x^2 - 8
<=> 5x + 9 = -8
<=> 5x = -8 - 9
<=> 5x = -17
<=> x = -17/5
4) (x - 2)^3 + (x - 5)(x + 5) = x(x^2 - 5x) - 7x + 3
<=> x^3 - 4x^2 + 4x - 2x^2 + 8x - 8 + x^2 - 5^2 = x^3 - 5x^2 - 7x + 3
<=> 12x - 33 = -7x + 3
<=> 19x - 33 = 3
<=> 19x = 3 + 33
<=> 19x = 36
<=> x = 36/19
5) (x + 4)(x^2 - 4x + 16) - x(x - 4)^2 = 8(x - 3)(x + 3)
<=> x^3 - 4x^2 + 16x + 4x^2 - 16x + 64 - x^3 + 8x^2 - 16x = 8x^2 - 72
<=> -16x + 64 = -72
<=> -16x = -72 - 64
<=> -16x = -136
<=> x = 136/16 = 17/2
6) 4(x - 1)(x + 2) - 5(x + 7) = (2x + 3)^2 - 5x + 3
<=> 4x^2 + 8x - 4x - 8 - 5x - 35 = 4x^2 + 12x + 9 - 5x + 3
<=> -x - 43 = 7x + 12
<=> -8x - 43 = 12
<=> -8x = 12 + 43
<=> -8x = 55
<=> x = -55/8
7) (x - 1)(x^2 + x + 1) + 3(x - 2)^2 = x(x^2 + 3x - 1)
<=> x^3 + x^2 + x - x^2 - x - 1 + 3x^2 - 12x + 12 = x^3 + 3x^2 - x
<=> 3x^2 - 12x + 11 = 3x^2 - x
<=> -12x + 11 = -x
<=> 11 = -x + 12x
<=> 11 = 11x
<=> x = 1
8) (x + 5)(x - 5) - (x + 3)(x^2 - 3x + 9) = 5 - x(x^2 - x - 2)
<=> x^2 - 25 - x^3 + 3x^2 - 9 - 3x^2 + 9x - 27 = 5 - x^3 + x^2 + 2x
<=> -52 - x^3 = 5 - x^3 + 2x
<=> -52 = 5x + 2x
<=> -5x - 2x = 52
<=> -7x = 52
<=> x = -52/7
9) (x + 2)^2 - 2(x + 3)(x - 4) = 5 - x(x - 3)
<=> x^2 + 4x + 4 - 2x^2 + 8x - 6x + 24 = 5 - x^3 + 3x
<=> 6x + 28 = 5 + 3x
<=> 6x + 28 - 3x = 5
<=> 3x + 28 = 5
<=> 3x = 5 - 28
<=> 3x = -23
<=> x = -23/3
10) (x + 7)(x - 7) - (x + 2)^2 = 5(x - 2) + (x - 7)
<=> x^2 - 49 - x^2 - 4x - 4 = 5x - 10 + x - 7
<=> -53 - 4x = 6x - 17
<=> -4x = 6x + 36
<=> -4x - 6x = 36
<=> -10x = 36
<=> x = -36/10 = -18/5
(4x-1)(3x+1)-5x2(x-3)-(x-4)(x-3)-7(x3-2x2+x-1)
=12x2+4x-3x-1-5x3+15x2-x2+3x+4x-12-7x3+14x2-7x+7
=-12x340x2+x-6
#H
(4x-1)(3x+1)-5x2(x-3)-(x-4)(x-3)-7(x3-2x2+x-1)
= 12x2+4x-3x-1-5x3+15x2-x2-3x-4x+12-7x3+14x2-7x-1
=-12x3+40x2-13x+10
(5x - 2)(x + 1) - 3x(x2 - x - 3) - 2x(x - 5)(x + 4) + 5x(x2 - 7)
= 5x2 + 3x - 2 - 3x3 + 3x2 + 9x - 2x(x2 - x - 20) + 5x3 - 35x
= 2x3 + 8x2 - 23x - 2 - 2x3 + 2x2 + 40x = 10x2 + 17x - 2
(x2 - 3x)(-5x2 + x) - x2(x - 7) + 5x2(x - 2)(x - 4) - (x + 1)(x + 3)
= -5x4 + 16x3 - 3x2 - x3 + 7x2 + 5x2(x2 - 6x + 8) - x2 - 4x - 3
= -5x4 + 15x3 + 3x2 - 4x - 3 + 5x4 - 30x3 + 40x2
= -15x3 + 43x2 - 4x - 3
1) a) A= (x+2)(\(x^2-2x+4\)) -(\(x^3-2\))
=(x+2)(\(x^2-2x+2^2\))-(\(x^3-2\))
= \(x^3+2^3\)-\(x^3+2\)
=(\(x^3-x^3\))+(\(2^3+2\))
=10
b) B= (a+2)(a-2)(\(a^2+2a+4\))(\(a^2-2a+4\))
= \(a^2-2^2\)+\(a^2+\left(2a\right)^2+4^2\)
=\(a^2-4+a^2+4a^2+16\)
=(\(a^2+a^2+4a^2\))+(-4+16)
=\(6a^2\)+12
(8x - 1)(2x - 3)) - (-x + 7)(x - 2) - 6x(x2 - x + 3) + (x2 - 3)(x - 4)
= 16x2 - 26x + 3 + x2 - 9x + 14 - 6x3 + 12x2 - 18x + x3 - 4x2 - 3x + 12
= -5x3 + 25x2 - 56x + 29
(8x - 1) (2x - 3) - (-x + 7)(x - 2) - 6x (x2 - x + 3) + (x2 - 3)(x - 4)
= 16x2-24x-2x-3+x2-2x-7x+14-6x3+6x-18x+x3-4x2-3x+12
=7x3+13x2-36x+23