Bài 1:

1. \(-10x^3y\left(\dfrac{2}{5}x^2y+\dfrac{3}{10}xy^2\right)+3x^4y^3=-4x^5y^2-3x^4y^3+3x^4y^3=-4x^5y^2\)

2.

a. \(A=85^2+170\cdot15+225=85^2+2\cdot85\cdot15+15^2=\left(85+15\right)^2=100^2=10000\)

Vậy A = 10000

b. \(B=20^2-19^2+18^2-17^2+...+2^2-1^2=\left(20^2-19^2\right)+\left(18^2-17^2\right)+...+\left(2^2-1^2\right)=\left(20-19\right)\left(20+19\right)+...+\left(2-1\right)\left(2+1\right)=39+35+31+27+23+19+15+11+7+3=\left(39+31+19+11\right)+\left(35+15+23+27\right)+\left(7+3\right)=100+100+10=210\)

Vậy B = 210

c. \(\left(15^4-1\right)\left(15^4+1\right)-3^8\cdot5^8=15^8-1-15^8=-1\)

Vậy C = -1

Bài 2:

Ta có: \(x^2-2x-y^2+1=\left(x^2-2x+1\right)-y^2=\left(x-1\right)^2-y^2=\left(x-y-1\right)\left(x+y-1\right)\)

\(\Rightarrow\left(x^2-2x-y^2+1\right):\left(x-y-1\right)=[\left(x-y-1\right)\left(x+y-1\right)]:\left(x-y-1\right)=x+y-1\)

Vậy \(\left(x^2-2x-y^2+1\right):\left(x-y-1\right)=x+y-1\)