Question

From the sum of $a+b-3c$and $b+c-a$ subtract the sum of $3c-8b+2a$and $-2c+5a-2b$

Answer 1

Find the sum of$a+b-3c$ and $b+c-a$ subtract the sum of $3c-8b+2a$and $-2c+5a-2b$

The sum of $a+b-3c$and $b+c-a$

$$\begin{gathered} a+b-3c+b+c-a=a-a+b+b-3c+c \\ =2b-2c \end{gathered}$$

$\therefore$The sum of $a+b-3c$ and $b+c-a$ is $2b-2c$

Then the sum of $3c-8b+2a$and $-2c+5a-2b$

$$\begin{gathered} 3c-8b+2a-2c+5a-2b=3c-2c-8b-2b+2a+5a \\ =c-10b+7a \end{gathered}$$

$\therefore$the sum of $3c-8b+2a$and $-2c+5a-2b$ is $c-10b+7a$

Now Subtract $c-10b+7a$ from $2b-2c$

$$\begin{gathered} (2b-2c)-(c-10b+7a)=2b-2c-c+10b-7a(Afterremovingthebracketthesignofsecondbracketchanged) \\ =-7a+2b+10b-2c-c \\ =-7a+12b-3c \end{gathered}$$

$\therefore$Final answer is$-7a+12b-3c$