Question

expressions-polynomials-evaluate add subtract polynomi
(1 point)
simplify the following expression
\\(\left2x^5 - 9x^4 + x^3 - \left(-5x^5 + 7x^4 - 3x^3\
ight)\
ight - \left-6x^5 - 8x^4 + x^3 + \left(-8x^5 - 7x^4 - 2x^3\
ight)\
ight\\)

Explanation:

Step1: Simplify the first bracket

First, simplify the expression inside the first bracket: \(2x^{5}-9x^{4}+x^{3}-(-5x^{5}+7x^{4}-3x^{3})\).
Distribute the negative sign: \(2x^{5}-9x^{4}+x^{3}+5x^{5}-7x^{4}+3x^{3}\).
Combine like terms: \((2x^{5}+5x^{5})+(-9x^{4}-7x^{4})+(x^{3}+3x^{3}) = 7x^{5}-16x^{4}+4x^{3}\).

Step2: Simplify the second bracket

Next, simplify the expression inside the second bracket: \(-6x^{5}-8x^{4}+x^{3}+(-8x^{5}-7x^{4}-2x^{3})\).
Distribute the positive sign (which doesn't change the terms): \(-6x^{5}-8x^{4}+x^{3}-8x^{5}-7x^{4}-2x^{3}\).
Combine like terms: \((-6x^{5}-8x^{5})+(-8x^{4}-7x^{4})+(x^{3}-2x^{3})=-14x^{5}-15x^{4}-x^{3}\).

Step3: Subtract the second bracket from the first

Now, subtract the simplified second bracket from the simplified first bracket: \((7x^{5}-16x^{4}+4x^{3})-(-14x^{5}-15x^{4}-x^{3})\).
Distribute the negative sign: \(7x^{5}-16x^{4}+4x^{3}+14x^{5}+15x^{4}+x^{3}\).
Combine like terms: \((7x^{5}+14x^{5})+(-16x^{4}+15x^{4})+(4x^{3}+x^{3}) = 21x^{5}-x^{4}+5x^{3}\).

Answer:

\(21x^{5}-x^{4}+5x^{3}\)