Question

Answer 1

1/ =6𝑥³−12𝑥²+18𝑥²−36𝑥

  =6𝑥³+6𝑥²−36𝑥

Answer 2

1) \(6x^2\left(x-2\right)+18x\left(x-2\right)=6x\left(x-2\right)\left(x+3\right)\)

2) \(5x^2+10xy+5y^2-45=5\left(x^2+2xy+y^2-9\right)=5\left[\left(x+y\right)^2-3^2\right]=5\left(x+y-3\right)\left(x+y+3\right)\)

3) \(2x^2-5x-7=2\left[x^2-\dfrac{5}{2}x+\dfrac{25}{16}-\dfrac{81}{16}\right]=2\left[\left(x-\dfrac{5}{4}\right)^2-\dfrac{81}{16}\right]=2\left(x-\dfrac{5}{4}-\dfrac{9}{4}\right)\left(x-\dfrac{5}{4}+\dfrac{9}{4}\right)=2\left(x-\dfrac{7}{2}\right)\left(x-1\right)=\left(2x-7\right)\left(x-1\right)\)

Answer 3

1: \(6x^2\left(x-2\right)+18x\left(x-2\right)=6x\left(x-2\right)\left(x+3\right)\)

2: \(5x^2+10xy+5y^2-45\)

\(=5\left[\left(x+y\right)^2-9\right]\)

\(=5\left(x+y-3\right)\left(x+y+3\right)\)

3: \(2x^2-5x-7=\left(2x-7\right)\left(x+1\right)\)