Question

Answer 1

2.1

a. 3x²y - 2xy²

= xy(3x - 2y)

b. x² - y² - 4x + 4

= x² - 4x + 4 - y²

= (x - 2)² - y²

= (x - 2 - y)(x - 2 + y)

Answer 2

2.1

a) \(3x^2y-2xy=xy\left(3x-2\right)\)

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

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

2.2

\(3x\left(x-2\right)-2+x=0\)

\(\Rightarrow3x\left(x-2\right)-\left(x-2\right)=0\)

\(\Rightarrow\left(x-2\right)\left(3x-1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{1}{3}\end{matrix}\right.\)