Question

Simplifying Expressions

3. Which of the following expressions is the simplified form of the expression below?
(x^3+2x^2+5) - (8x^2 - 4x + 6)
A. 10x -11
B. 9x^3-- 2x^2 +11
C. 7x^2 - 2x^2 -1
D. x^3-6x^2+ 4x - 1

Answer 1

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.

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.