Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
1.
a. \((x+1)(x^2-x+1)-(x-1)(x^2+x+1)\)
\(=x^3 + 1-(x^3-1) = 2 \)
b.
\(\dfrac{2x^2-4x+2}{2x-2}=\dfrac{2\left(x^2-2x+1\right)}{2\left(x-1\right)}=\dfrac{\left(x-1\right)^2}{x-1}=x-1\)
2.
a. \(x^2-4y^2+12y-9=x^2-\left[\left(2y\right)^2-2\cdot2y\cdot3+3^2\right]=x^2-\left(2y-3\right)^2=\left(x-2y+3\right)\left(x+2y-3\right)\)
b.
\(5x^2+3\left(x+y\right)^2-5y^2\)
\(=3\left(x+y\right)^2+5\left(x^2-y^2\right)\)
\(=3\left(x+y\right)^2+5\left(x+y\right)\left(x-y\right)\)
\(=\left(x+y\right)\left[3\left(x+y\right)+5\left(x-y\right)\right]\)
\(=\left(x+y\right)\left(3x+3y+5x-5y\right)\)
\(=\left(x+y\right)\left(8x-2y\right)=2\left(x+y\right)\left(4x-y\right)\)
a: \(\dfrac{7x^3y^4}{35xy}=\dfrac{7xy\cdot x^2y^3}{7xy\cdot5}=\dfrac{x^2y^3}{5}\)
b: \(\dfrac{x^3-4x}{10-5x}=\dfrac{-x\left(x-2\right)\left(x+2\right)}{5\left(x-2\right)}=\dfrac{-x\left(x+2\right)}{5}=\dfrac{-x^2-2x}{5}\)
c: \(\dfrac{\left(x+2\right)\left(x+1\right)}{x^2-1}=\dfrac{\left(x+2\right)\left(x+1\right)}{\left(x+1\right)\left(x-1\right)}=\dfrac{x+2}{x-1}\)
d: \(\left(x^2-x-2\right)\left(x-1\right)\)
\(=\left(x-2\right)\left(x+1\right)\left(x-1\right)\)
\(=\left(x^2-3x+2\right)\left(x+1\right)\)
=>\(\dfrac{x^2-x-2}{x+1}=\dfrac{x^2-3x+2}{x-1}\)
e: \(\dfrac{x^3+8}{x^2-2x+4}=\dfrac{\left(x+2\right)\left(x^2-2x+4\right)}{x^2-2x+4}=x+2\)
Chọn B