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a) (2x - 1)(3x + 5) - 2(-4x + 1)2 = 6x2 + 10x - 3x - 5 - 2(16x2 - 8x + 1) = 6x2 - 3x - 5 - 32x2 + 16x - 2 = -26x2 + 13x - 7
b) \(\frac{x^2-16}{4x-x^2}=\frac{\left(x-4\right)\left(x+4\right)}{-x\left(x-4\right)}=-\frac{x+4}{x}\)
c) \(\frac{2x-9}{x^2-5x+6}+\frac{2x+1}{x-3}+\frac{x+3}{2-x}\)
= \(\frac{2x-9}{x^2-2x-3x+6}+\frac{\left(2x+1\right)\left(x-2\right)}{\left(x-3\right)\left(x-2\right)}-\frac{\left(x+3\right)\left(x-3\right)}{\left(x-3\right)\left(x-2\right)}\)
= \(\frac{2x-9+2x^2-3x-2-x^2+9}{\left(x-3\right)\left(x-2\right)}\)
= \(\frac{x^2-x-2}{\left(x-3\right)\left(x-2\right)}\)
= \(\frac{x^2-2x+x-2}{\left(x-3\right)\left(x-2\right)}\)
= \(\frac{\left(x+1\right)\left(x-2\right)}{\left(x-3\right)\left(x-2\right)}=\frac{x+1}{x-3}\)
d) (x - 1)3 - (x + 1)3 + 6(x + 1)(x - 1)
= (x - 1 - x - 1)[(x - 1)2 + (x - 1)(x + 1) + (x + 1)2] + 6(x2 - 1)
= -2(x2 - 2x + 1 + x2 - 1 + x2 + 2x + 1) + 6x2 - 6
= -2(3x2 + 1) + 6x2 - 6
= -6x2 - 2 + 6x2 - 6
= -8
e) (2x + 7)2 - (4x + 14)(2x - 8) + (8 - 2x)2
= (2x + 7)2 - 2(2x + 7)(2x - 8) + (2x - 8)2
= (2x + 7 - 2x + 8)2
= 152 = 225
(-3x + 4)(x - 2) - x(x2 - 2)(-4x + 1) + (2x - 5)(x2 - 4x)
= -3x2 + 10x - 8 - x(-4x3 + x2 + 8x - 2) + 2x3 - 13x2 + 20x
= 2x3 - 16x2 + 30x - 8 + 4x4 - x3 - 8x2 + 2x
= 4x4 + x3 - 24x2 + 28x - 8
-7x(2x2- 4x - 5) - (x - 5)(-2x + 3) + (3x - 2)(x+4) - 4x2 (x - 3)
=-14x3+28x2+35x+2x2-3x-10x+15+3x2+12x-2x-8-4x3+12x2
=-18x3+45x2+32x+7
4x(x2-2x+3)-3x(x+1)(x-2)+(2x-5)(x-7)-4x(x2-x+1)
=4x3-8x2+12x-3x(x2-2x+x-2)+2x2-14x-5x+35-4x3+4x2-4x
=4x3-8x2+12x-3x3+6x2-3x2+6x+2x2-14x-5x+35-4x3+4x2-4x
=-3x3+x2-5x+35
#H