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What is the standard form polynomial that represents this product?
(-2m³ +3m² m)(4m² + m - 5)
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Answer 1

To find the standard form of the polynomial resulting from the product (-2m³ + 3m²m)(4m² + m - 5), you multiply each term of the first polynomial by each term of the second, then combine like terms to get 4m⁵ + m⁴ - 5m³.

Step-by-step explanation:

The question asks for the standard form of the polynomial that represents the product of the two given polynomials: (-2m³ + 3m²m)(4m² + m - 5). To find this, we'll need to perform polynomial multiplication, which involves distributing each term of the first polynomial by each term of the second polynomial.

First, distribute -2m³ across all the terms of the second polynomial:

• -2m³ × 4m² = -8m⁵
• -2m³ × m = -2m⁴
• -2m³ × (-5) = 10m³

Next, distribute 3m²m (which simplifies to 3m³) across all the terms of the second polynomial:

• 3m³ × 4m² = 12m⁵
• 3m³ × m = 3m⁴
• 3m³ × (-5) = -15m³

Combine like terms to obtain the standard form of the polynomial:

• -8m⁵ + 12m⁵ = 4m⁵
• -2m⁴ + 3m⁴ = m⁴
• 10m³ - 15m³ = -5m³

The final answer in standard form is 4m⁵ + m⁴ - 5m³.