Question

Rewrite the expression -2a(a+b-5)+3(-5a+2b)+b(6a+b-8)

Answer 1

First, think of it as 3 different expressions.Go through them one at a time. There is:
-2a(a+b-5)                    ]            +3(-5a+2b)          ]        +b(6a+b-8)
Multiply everything out.] Multiply everything out.  ]Multiply everything out
-2a x a = -2a²               ] +3 x -5a = -15a               ] +b x 6a = 6ab 
-2a x b = -2ab              ] +3 x 2b = 6b                    ] +b x b = b²
-2a x -5 = 10a              ] -15a + 2b = -15a+2b       ] +b x -8 = -8b                  -2a² + -2ab + 10a =  ]                                         ] 6ab + b² + -8b =
-2a²+-2ab+10a            ]                                         ] 6ab+b²+-8b
Now add everything up, but before that, remember these algebraic rules:
∞A.S.S. Add Same Signs, meaning positive add positive or negative add negative equals a positive number or 0. E.g 1+1=1 and -1+-2= 1
∞S.I.D. Subtract If Different, meaning a positive number add a negative number always equals a negative number or 0. E.g 1 + -2 = -1
∞You can only add up "similar terms", meaning you can add 'terms' ending in 'a' for example with another 'term' ending in 'a'. However. you cannot add a term ending in 'a' to an 'ab' or an 'a²'.
Following these rules, -2a²+-2ab+10a+-15a+2b+6ab+b²+-8b = 
4ab-5a-6b+b²-2a²

Hope that helps you and that it wasn't too tricky to understand. :)