Question

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

a) \(x^2+6x+9\)

b) \(x^2+x+\dfrac{1}{4}\)

c) \(2xy^2+x^2y^4+1\)

Answer 1

a) x²+6x+9=x²+2.x.3+3²=(x+3)²

b) x²+x+\(\dfrac{1}{4}\)=x²+2.x.\(\dfrac{1}{2}\)+\(\dfrac{1}{4}\)=(x+\(\dfrac{1}{2}\))²

c) 2xy²+x²y⁴+1=(xy²)²+2.xy²+1=(xy²+1)²

Answer 2

a,(x+3)^2

b,(x+1/2)^2

Answer 3

a) (x+3)²

b) (x+\(\dfrac{1}{2}\))²

c) (xy²+1)²

Answer 4

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

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

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