Question

Rút gọn các biểu thức sau a)(căn1-4a+4a^2 ) -2a b)x-2y-căn x^2-4xy+4y^2

Answer 1

a) \(\sqrt[]{1-4a+4a^2}\)

\(=\sqrt[]{\left(1-2a\right)^2}\)

\(=\left|1-2a\right|\)

\(=\left[{}\begin{matrix}1-2a\left(a\le\dfrac{1}{2}\right)\\2a-1\left(a>\dfrac{1}{2}\right)\end{matrix}\right.\)

b) \(x-2y-\sqrt[]{x^2-4xy+4y^2}\)

\(=x-2y-\sqrt[]{\left(x-2y\right)^2}\)

\(=x-2y-\left|x-2y\right|\)

\(=\left[{}\begin{matrix}x-2y-x+2y\left(x\ge2y\right)\\x-2y+x-2y\left(x< 2y\right)\end{matrix}\right.\)

\(=\left[{}\begin{matrix}0\left(x\ge2y\right)\\2x-4y\left(x< 2y\right)\end{matrix}\right.\)

\(=\left[{}\begin{matrix}0\left(x\ge2y\right)\\2\left(x-2y\right)\left(x< 2y\right)\end{matrix}\right.\)