Answer:
The sum of the terms is equal to [tex]5r^2-14r+3s[/tex].
The value of the sum at [tex]r=1,s=3[/tex] is 0.
Step-by-step explanation:
Given:
The terms that are given are:
[tex]10r^2, -6r, +5s, -8r, +2s, -5r^2, -4s[/tex]
The sum of the terms is the addition of the given terms and is given as:
[tex]=10r^2+ (-6r)+5s+ (-8r)+2s + (-5r^2) + (-4s)[/tex]
[tex]=10r^2-6r+5s-8r+2s-5r^2-4s[/tex]
Now, combining like terms. Like terms means that are of the same type are grouped together. There are 3 different terms here 'r²', 'r' and 's'.
The terms containing 'r²' are: [tex]10r^2, -5r^2[/tex]
The terms containing 'r' are: [tex]-8r, -6r[/tex]
The terms containing 's' are: [tex]5s, 2s, -4s[/tex]
Now, combining the like terms, we get:
[tex]=(10r^2-5r^2)+(-8r-6r)+(5s + 2s -4s)[/tex]
[tex]=(10-5)r^2+(-8-6)r+(5+2-4)s[/tex]
[tex]=5r^2+(-14)r+3s[/tex]
[tex]=5r^2-14r+3s[/tex]
Therefore, the final expression is equal to:
[tex]=5r^2-14r+3s[/tex]
Now, plug in [tex]r=1,s=3[/tex]. This gives,
[tex]=5(1)^2-14(1)+3(3)[/tex]
[tex]=5\times 1-14+9[/tex]
[tex]=5-14+9[/tex]
[tex]=0[/tex]
Therefore, the value of the sum of all the terms at [tex]r=1,s=3[/tex] is 0.
