Question

instructions
solve the following problem and choose the best answer.

question
\\((-2y^5 + y^3 - 2y) - (y^5 - 4y^3 + 6) =\\)

\\(\circ -3y^5 - 3y^3 + 4y\\)
\\(\circ -3y^5 - 3y^3 - 2y - 6\\)
\\(\circ -3y^5 + 5y^3 + 4y\\)
\\(\circ -3y^5 + 5y^3 - 2y - 6\\)

Explanation:

Distribute the negative sign

To subtract the second polynomial, distribute the negative sign to each term inside the second set of parentheses.

$$ -(y^5 - 4y^3 + 6) = -y^5 + 4y^3 - 6 $$

Rewrite the entire expression

Combine the first polynomial with the newly distributed terms of the second polynomial.

$$ -2y^5 + y^3 - 2y - y^5 + 4y^3 - 6 $$

Group like terms

Group terms with the same exponents together to prepare for simplification.

$$ (-2y^5 - y^5) + (y^3 + 4y^3) - 2y - 6 $$

Combine like terms

Simplify the coefficients for each group of like terms.

$$ -3y^5 + 5y^3 - 2y - 6 $$

Answer:

• (A) \(-3y^5 - 3y^3 + 4y\)
• (B) \(-3y^5 - 3y^3 - 2y - 6\)
• (C) \(-3y^5 + 5y^3 + 4y\)
• (D) \(-3y^5 + 5y^3 - 2y - 6\) (Correct answer)