Question

simplify the expressions. be sure to write your answer in stan
$(-14x^{9}+9x^{3}+2x)+(3x^{9}-5x^{6}-x)$

$(2x^{3}+5x^{2}-8)+(x^{3}-3x+2)$

$(x + 2)(x^{2}-8x + 7)$

$5x(x^{3}-2y)$

Explanation:

First Expression: \((-14x^{9} + 9x^{3} + 2x) + (3x^{9} - 5x^{6} - x)\)

Step1: Remove parentheses

\(-14x^{9} + 9x^{3} + 2x + 3x^{9} - 5x^{6} - x\)

Step2: Combine like terms for \(x^9\)

\((-14x^{9}+3x^{9}) - 5x^{6}+ 9x^{3}+(2x - x)\)
\(=-11x^{9}- 5x^{6}+ 9x^{3}+x\)

Step1: Remove parentheses

\(2x^{3} + 5x^{2} - 8 + x^{3} - 3x + 2\)

Step2: Combine like terms for \(x^3\) and constants

\((2x^{3}+x^{3})+ 5x^{2}- 3x+(-8 + 2)\)
\(=3x^{3}+ 5x^{2}- 3x - 6\)

Step1: Distribute \(x\) and \(2\)

\(x(x^{2}-8x + 7)+2(x^{2}-8x + 7)\)
\(=x^{3}-8x^{2}+7x + 2x^{2}-16x + 14\)

Step2: Combine like terms

\(x^{3}+(-8x^{2}+2x^{2})+(7x - 16x)+14\)
\(=x^{3}-6x^{2}-9x + 14\)

Answer:

\(-11x^{9}- 5x^{6}+ 9x^{3}+x\)

Second Expression: \((2x^{3} + 5x^{2} - 8) + (x^{3} - 3x + 2)\)