Question

Đưa về bình phương của 1 tổng hoặc hiệu
\(1-4x+x^2\)
\(x^2-x+\frac{1}{4}\)
\(\left(x-y\right)^2-2\left(x+y\right)\left(x+y\right)+\left(x+y\right)^2\)

Answer 1

a) Sửa đề: \(1-4x+4x^2\)

Ta có: \(1-4x+4x^2\)

\(=1^2-2\cdot1\cdot2x+\left(2x\right)^2\)

\(=\left(1-2x\right)^2\)

b) Ta có: \(x^2-x+\frac{1}{4}\)

\(=x^2-2\cdot x\cdot\frac{1}{2}+\left(\frac{1}{2}\right)^2\)

\(=\left(x-\frac{1}{2}\right)^2\)

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

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

\(=\left(-2y\right)^2=4y^2\)