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Step-by-step explanation:
The given equation, m³ + n³ = (m + n)(m² - mn + n²), is known as the sum of cubes formula. It is a well-known identity in algebra that allows us to expand the sum of cubes of two numbers, m and n.
To understand how this formula works, let’s expand the right-hand side of the equation:
(m + n)(m² - mn + n²) = m(m² - mn + n²) + n(m² - mn + n²)
Now, let’s expand each term:
m(m² - mn + n²) = m³ - m²n + mn²
n(m² - mn + n²) = nm² - mn² + n³
Combining these two expanded terms, we get:
m³ + n³ = (m + n)(m² - mn + n²)
As we can see, the sum of cubes of m and n is equal to the product of (m + n) and (m² - mn + n²). This formula is often used in various mathematical applications, such as simplifying expressions and solving equations involving cubes.