Question

Subtract: $\frac{1}{2}x-2\sqrt{5}{x}^2+\frac{1}{\sqrt{5}}{x}^3$ from $\frac{3}{2}x-4\sqrt{5}{x}^2+\frac{1}{\sqrt{5}}{x}^3$

• A. $x-2\sqrt{5}{x}^2$
• B. $2\sqrt{5}{x}^2$
• C. $x+2\sqrt{5}{x}^2$
• D. None of these

Answer 1

Answer: (A)

$x-2\sqrt{5}{x}^2$

We find the subtraction of the given polynomials $(\frac{3}{2}x-4\sqrt{5}{x}^2+\frac{1}{\sqrt{5}}{x}^3)-(\frac{1}{2}x-2\sqrt{5}{x}^2+\frac{1}{\sqrt{5}}{x}^3)$ by combining the like terms as shown below:

$(\frac{3}{2}x-4\sqrt{5}{x}^2+\frac{1}{\sqrt{5}}{x}^3)-(\frac{1}{2}x-2\sqrt{5}{x}^2+\frac{1}{\sqrt{5}}{x}^3)=(\frac{1}{\sqrt{5}}{x}^3-\frac{1}{\sqrt{5}}{x}^3)+(-4\sqrt{5}{x}^2+2\sqrt{5}{x}^2)+(\frac{3}{2}x-\frac{1}{2}x)=x^3(\frac{1}{\sqrt{5}}-\frac{1}{\sqrt{5}})+x^2(-4\sqrt{5}+2\sqrt{5})+x(\frac{3}{2}-\frac{1}{2})=-2\sqrt{5}{x}^2+x$

Hence, $(\frac{3}{2}x-4\sqrt{5}{x}^2+\frac{1}{\sqrt{5}}{x}^3)-(\frac{1}{2}x-2\sqrt{5}{x}^2+\frac{1}{\sqrt{5}}{x}^3)=x-2\sqrt{5}{x}^2$.