a, $\left(x-y\right)\left(x^2+xy+y^2\right)$

$=x^3+x^2y+xy^2-x^2y-xy^2-y^3=x^3-y^3$

b, $\left(a^3-2a^2+a-1\right)\left(a-5\right)$

$=a^4-2a^3+a^2-a-5a^3+10a^2-5a+5$

$=a^4-7a^3+11a^2-6a+5$

c, $\left(x^2-2x+y^2\right)\left(x-y\right)-3xy\left(y-x\right)$

$=x^3-2x^2+xy^2-x^2y+2xy-y^3-3xy^2+3x^2y$

$=x^3-2x^2-2xy^2-2x^2y+2xy-y^3$

Bài 2:

a, $\left(12x-5\right)\left(x+1\right)+\left(6x-2\right)\left(3-2x\right)=5$

$\Rightarrow12x^2+12x-5x-5+18x-12x^2-6+4x=5$

$\Rightarrow29x=5+5+6$

$\Rightarrow29x=16\Rightarrow x=\dfrac{16}{29}$

b, $\left(x-5\right)\left(2x+3\right)-2x\left(x-3\right)+x+7=-8$

$\Rightarrow2x^2+3x-10x-15-2x^2+6x+x+7=-8$

$\Rightarrow0x=-8\Rightarrow x\in\varnothing$

Chúc bạn học tốt!!!

Tính (5x3-x2+2x-3)(4x2-x+2)

(5x3-x2+2x-3)(4x2-x+2)

= 20x5-5x4+10x3-4x4+x3-2x2+8x3-2x2+4x-12x2+3x-6

= 20x5 - 9x4 + 19x3 - 16x2 + 7x - 6