Question

Bài 1: Viết các đơn thức sau thành tích

a) x^2-4x+4

b) x^2-4y^2

c)4x^2-4x+1

d) x^3-3x^2+3x-1

e) 4x^2-9

g) 4x^2+12xy+9y^2

Answer 1

a. \(x^2-4x+4=x^2-2.x.2+2^2=\left(x-2\right)^2\)

b. \(x^2-4y^2=x^2-\left(2y\right)^2=\left(x-2y\right)\left(x+2y\right)\)

c. \(4x^2-4x+1=\left(2x\right)^2-2.2x.1+1^2=\left(2x-1\right)^2\)

d. \(x^3-3x^2+3x-1\)

\(=x^3-1^3-3x^2+3x\)

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

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

\(=\left(x-1\right)\left(x^2-4x+1\right)\)

e. \(4x^2-9=\left(2x\right)^2-3^2=\left(2x-3\right)\left(2x+3\right)\)

g. \(4x^2+12xy+9y^2=\left(2x\right)^2+2.2x.3y+\left(3y\right)^2=\left(2x+3y\right)^2\)