Question

Subtract the sum of (7pq - 3qr + 4rs) and (9qr + 3rs - 5pq) from the sum of (29r - 4rs + 6pq) and (11pq-3qr+5rs).​

Answer 1

Answer:

Subtract sum of ( 7pq - 3qr + 4rs ) and ( 9qr + 3rs - 5pq ) from the sum of ( 29qr - 4rs + 6pq ) and ( 11pq - 3qr + 5rs)

First lets calculate the sum of ( 7pq - 3qr + 4rs ) and ( 9qr + 3rs - 5pq )

→ ( 7pq -3qr + 4rs + 9qr + 3rs - 5pq )

Add all the pq terms together. Similarly add all qr and rs terms together.

→ ( 7pq - 5pq -3qr + 9qr + 4rs + 3rs )

→ ( 2pq + 6qr + 7rs )

This is the sum of ( 7pq - 3qr + 4rs ) and ( 9qr + 3rs - 5pq ).

Now lets calculate the sum of  ( 29qr - 4rs + 6pq ) and ( 11pq - 3qr + 5rs)

→ ( 29 qr - 4rs + 6pq + 11pq - 3qr + 5rs )

Adding all pq terms, qr terms are rs terms together we get:

→ ( 11pq + 6pq + 29qr - 3qr - 4rs + 5rs )

→ ( 17pq + 26qr + 1rs )

This is the sum of  ( 29qr - 4rs + 6pq ) and ( 11pq - 3qr + 5rs)

Now according to the question we have to subtract ( 2pq + 6qr + 7rs ) from ( 17pq + 26qr + 1rs ). Hence we get:

→ ( 17pq + 26qr + 1rs ) - ( 2pq + 6qr + 7rs )

→ ( 17pq - 2pq + 26qr - 6qr + 1rs - 7rs )

→ ( 15pq + 20qr - 6rs )

This is the required answer.

Answer 2

Question:-

Subtract the sum of (7pq - 3qr + 4rs) and (9qr + 3rs - 5pq) from the sum of (29r - 4rs + 6pq) and (11pq-3qr+5rs)

Answer:-

Sum of (7pq - 3qr + 4rs) and (9qr + 3rs - 5pq) :-

(7pq - 3qr + 4rs) + (9qr + 3rs - 5pq)

=> 7pq - 3qr + 4rs + 9qr + 3rs - 5pq

=> 7pq - 5pq + 9qr - 3qr + 4rs + 3rs

=> 2pq + 6qr + 7rs

Sum of (29qr - 4rs + 6pq) and (11pq-3qr+5rs) :-

(29qr - 4rs + 6pq) + (11pq-3qr+5rs)

=> 29qr - 4rs + 6pq + 11pq - 3qr + 5rs

=> 29qr - 3qr + 5rs - 4rs + 6pq + 11pq

=> 26qr + rs + 17pq

Subtracting their sum :-

[ "From" number comes first. ]

[ Original signs are changed to opposite sign while removing the bracket if there is minus sign before the bracket ]

=> (26qr + rs + 17pq) - (2pq + 6qr + 7rs)

=> 26qr + rs + 17pq - 2pq - 6qr - 7rs

=> 26qr - 6qr - 7rs + rs + 17pq - 2pq

=> 20qr - 6rs + 15pq

Ans. 20qr - 6rs + 15pq