To solve the given equation (a² - b²)m + (b² - a²)n - (5a² - 5b²)q = (a + b)(a - b), we can simplify the terms step by step:
First, expand the expressions:
(a² - b²)m + (b² - a²)n - (5a² - 5b²)q = (a + b)(a - b)
am² - bm² + bn² - an² - 5aq² + 5bq² = a² - b²
Next, simplify further by grouping like terms:
am² - bn² - an² + bn² - 5aq² + 5bq² = a² - b²
am² - an² - 5aq² + 5bq² = a² - b²
Now, factor out the common terms:
a(m - n - 5q²) + 5q²(b - a) = a² - b²
Finally, simplify the remaining terms:
a(m - n - 5q²) - 5q²(a - b) = a² - b²
Therefore, the solution to the equation is:
a(m - n - 5q²) - 5q²(a - b) = a² - b².
