Question

21. \(x^2\)- 3x\(\sqrt{y}\)+ 2y

22. x + 2\(\sqrt{x-1}\)

23. \(\sqrt{x^3}\)- 2\(\sqrt{x}\)-x

24. -6x + 5\(\sqrt{x}\)+ 1

Answer 1

22: \(x+2\sqrt{x-1}=\left(\sqrt{x-1}+1\right)^2\)

24: \(-6x+5\sqrt{x}+1=\left(\sqrt{x}-1\right)\left(-6\sqrt{x}-1\right)\)

Answer 2

21: \(x^2-3x\sqrt{y}+2y\)

\(=x^2-x\sqrt{y}-2x\sqrt{y}+2y\)

\(=x\left(x-\sqrt{y}\right)-2\sqrt{y}\left(x-\sqrt{y}\right)\)

\(=\left(x-\sqrt{y}\right)\left(x-2\sqrt{y}\right)\)

23: \(\sqrt{x^3}-2\sqrt{x}-x\)

\(=x\sqrt{x}-2\sqrt{x}-x\)

\(=\sqrt{x}\left(x-\sqrt{x}-2\right)\)

\(=\sqrt{x}\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)\)