Question

(m²+2n³)(m⁴-2m²n³+4n^6)

Answer 1

Это сумма кубов
(m²+2n³)(m⁴-2m²n³+4n⁶) = (m²+2n³)((m²)²-m²*2n³+(2n³)²) = (m²)³+(2n³)³ = 
= m⁶+8n⁹

Answer 2

To expand the expression (m² + 2n³)(m⁴ - 2m²n³ + 4n^6), you can use the distributive property, also known as FOIL (First, Outer, Inner, Last). Here's how you can do it:

First, you multiply the first terms in each expression: (m²) * (m⁴) = m⁶

Next, you multiply the outer terms: (m²) * (-2m²n³) = -2m⁴n³

Then, you multiply the inner terms: (2n³) * (m⁴) = 2m⁴n³

Finally, you multiply the last terms in each expression: (2n³) * (-2m²n³) = -4n⁶

Now, you can add all these results together to get the expanded expression: m⁶ - 2m⁴n³ + 2m⁴n³ - 4n⁶

Notice that the middle terms with 2m⁴n³ and -2m⁴n³ cancel each other out. So, the expanded expression simplifies to:

m⁶ - 4n⁶