Question

Written as a simplified polynomial in standard form, what is
the result when (2x – 5)2 is subtracted from x-10?

Answer 1

Answer:

$\left(x-10\right)-\left(2x-5\right)^2=-4x^2+21x-35$

Step-by-step explanation:

As we have to subtract $\left(2x\:-\:5\right)^2$ from $\left(x-10\right)$

so

$\left(x-10\right)-\left(2x\:-\:5\right)^2$

solving and simplifying the polynomial in standard form

$\left(x-10\right)-\left(2x-5\right)^2$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$=x-10-\left(2x-5\right)^2$

$=x-10-\left(4x^2-20x+25\right)$      ∵ $\left(2x\:-\:5\right)^2=\:4x^2-20x+25$

$=x-10-4x^2+20x-25$

$=-4x^2+21x-35$

We know that standard form means that the terms of the expression are ordered from biggest exponent to lowest exponent.

Thus, a simplified polynomial in standard form is:

$\left(x-10\right)-\left(2x-5\right)^2=-4x^2+21x-35$