Question

1. multiply \\(-2x^{-3}y(5yx^5 + 8xy - 4y^2x^2)\\).

\\(-10x^2y^2 - 16x^{-2}y^2 + 8x^{-1}y^3\\)

\\(-28x^{-1}y^7\\)

\\(-10x^{-2}y^6 - 16x^{-2}y^2 + 8x^{-1}y^3\\)

\\(-10x^2y^2 - 16x^{-2}y^2 - 8x^{-1}y^3\\)

Explanation:

Distribute the monomial to each term in the trinomial

$$ -2x^{-3}y(5yx^5 + 8xy - 4y^2x^2) = (-2x^{-3}y)(5yx^5) + (-2x^{-3}y)(8xy) - (-2x^{-3}y)(4y^2x^2) $$

Apply exponent rules to simplify each product

$$
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$$

Combine the simplified terms

$$ -10x^2y^2 - 16x^{-2}y^2 + 8x^{-1}y^3 $$

Answer:

• (A) \(-10x^2y^2 - 16x^{-2}y^2 + 8x^{-1}y^3\) (Correct answer)
• (B) \(-28x^{-1}y^7\)
• (C) \(-10x^{-2}y^6 - 16x^{-2}y^2 + 8x^{-1}y^3\)
• (D) \(-10x^2y^2 - 16x^{-2}y^2 - 8x^{-1}y^3\)