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!!!