Question

Viết các biểu thức sau đây dưới dạng bình phương của một tổng hoặc một hiệu

a)\(9x^2+6x+1\)

b)\(x^2-x+\frac{1}{4}\)

c)\(x^2.y^4-2xy^2+1\)

d)\(x^2+\frac{2}{3}x+\frac{1}{9}\)

Answer 1

a) \(9x^2+6x+1=\left(3x\right)^2+2.3x.1+1^2=\left(3x+1\right)^2\)

b) \(x^2-x+\dfrac{1}{4}=x^2-2.\dfrac{1}{2}x+\left(\dfrac{1}{2}\right)^2=\left(x-0,5\right)^2\)

c) \(x^2y^4-2xy^2+1=\left(xy^2\right)^2-2.xy^2.1+1^2=\left(xy^2-1\right)^2\)

d) \(x^2+\dfrac{2}{3}x+\dfrac{1}{9}=x^2+2.x.\dfrac{1}{3}+\left(\dfrac{1}{3}\right)^2=\left(x+\dfrac{1}{3}\right)^2\)

Answer 2

a) \(9x^2+6x+1\)

\(=\left(3x\right)^2+2.3x.1+1^2\)

\(=\left(3x+1\right)^2\)

Answer 3

b) \(x^2-x+\dfrac{1}{4}\)

\(=x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2\)

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

Answer 4

c) \(x^2y^4-2xy^2+1\)

\(=\left(xy^2\right)^2-2.xy^2.1+1^2\)

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

Answer 5

d) \(x^2+\dfrac{2}{3}x+\dfrac{1}{9}\)

\(=x^2+2.x.\dfrac{1}{3}+\left(\dfrac{1}{3}\right)^2\)

\(=\left(x+\dfrac{1}{3}\right)^2\)