Question

Subtract the difference of (2a-3b+8) and (a+2b+6) from the sum of (8a-5b+3) and (6a+3b+5) .

Answer 1

First let find the sum of first two given algebraic expressions
Let P=(8a-5b+3)+(6a+3b+5)
=8a-5b+3+6a+3b+5
=(8a+6a)+(-5b+3b)+(3+5)
=14a+(-2b)+8
=14a-2b+8
Now calculate the difference of the last two given expressions:
Let Q=(2a-3b+8)-(a+2b+6)
=2a-3b+8-a-2b-6
=(2a-a)+(-3b-2b)+(8-6)
=a+(-5b)+2
=a-5b+2
Now,
P-Q=(14a-2b+8)-(a-5b+2)
=14a-2b+8-a+5b-2
=(14a-a)+(-2b+5b)+(8-2)
=13a+3b+6