Question

At the end of the year 2016, the population of villages Kovad, Varud, Chikhali is 5x² - 3y², 7y² + 2xy and 9x² + 4xy respectively. At the beginning of the year 2017, x² + xy - y², 5xy and 3x² + xy persons from each of the three villages respectively went to another village for education then what is the remaining total population of these three villages?

Answer 1

Total population of the three villages

= (5x² - 3y²) + (7y² + 2xy) + (9x² + 4xy)

= 5x² + 9x² - 3y² + 7y² + 2xy + 4xy

= 14x² + 4y² + 6xy

Total number of persons who went to another village for education

= (x² + xy - y²) + 5xy + (3x² + xy)

= x² + 3x² - y² + xy + 5xy + xy

= 4x² - y² + 7xy

∴ Remaining total population of the three villages = Total population of the three villages − Total number of persons who went to another village for education

= (14x² + 4y² + 6xy) - (4x² - y² + 7xy)

= 14x² + 4y² + 6xy - 4x² + y² - 7xy

= 14x² - 4x² + 4y² + y² + 6xy - 7xy

= 10x² + 5y² - xy

Thus, the remaining total population of these three villages is 10x² + 5y² − xy.