Question

Simplifying Expressions

Answer 1

Answer:

As

$\left(x^3+2x^2+5\right)-\left(8x^2-4x+6\right)=x^3-6x^2+4x-1$

Therefore, option D is the correct answer is.

Step-by-step explanation:

Given the expression

$\left(x^3+2x^2+5\right)\:-\:\left(8x^2\:-\:4x\:+\:6\right)$

solving to simplify the expression

$\left(x^3+2x^2+5\right)\:-\:\left(8x^2\:-\:4x\:+\:6\right)$

$=x^3+2x^2+5-\left(8x^2-4x+6\right)$        ∵  $\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$=x^3+2x^2+5-\left(8x^2-4x+6\right)$

$=x^3+2x^2+5-8x^2+4x-6$

Group like terms

$=x^3+2x^2-8x^2+4x+5-6$

$\mathrm{Add\:similar\:elements:}\:2x^2-8x^2=-6x^2$

$=x^3-6x^2+4x+5-6$

$\mathrm{Add/Subtract\:the\:numbers:}\:5-6=-1$

$=x^3-6x^2+4x-1$

Therefore, the simplified form of the expression is

$\left(x^3+2x^2+5\right)-\left(8x^2-4x+6\right)=x^3-6x^2+4x-1$

Therefore, option D is the correct answer is.