Question

When you subtract the sum of 3p - 7q + 8r and 2p + 3q - 5r from the sum of p + q + r and 4p - 3q - 2r, the result is:​

Answer 1

Sum of 3p - 7q + 8r and 2p + 3q - 5r

= 3p - 7q + 8r + 2p + 3q - 5r

= (3 + 2)p + (-7 + 3)q + (8 - 5)r

= p - 4q + 3r

Sum of p + q + r and 4p - 3q - 2r

= p + q + r + 4p - 3q - 2r

= (1 + 4)p + (1 - 3)q + (1 - 2)r

= 5p - 2p - r

Subtract p - 4q + 3r from 5p - 2p - r

= 5p - 2p - r - (p - 4q + 3r)

= 5p - 2p - r - p + 4q - 3r

= (5 - 1)p + (-2 + 4)q + (-1 - 2)r

= 4p + 2q - 3r