Question

Indicate the sum of the terms in each of the following examples, and simplify the result by combining like terms:

Answer 1

Answer:

The sum of the terms is equal to $5r^2-14r+3s$.

The value of the sum at $r=1,s=3$ is 0.

Step-by-step explanation:

Given:

The terms that are given are:

$10r^2, -6r, +5s, -8r, +2s, -5r^2, -4s$

The sum of the terms is the addition of the given terms and is given as:

$=10r^2+ (-6r)+5s+ (-8r)+2s + (-5r^2) + (-4s)$

$=10r^2-6r+5s-8r+2s-5r^2-4s$

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: $10r^2, -5r^2$

The terms containing 'r' are: $-8r, -6r$

The terms containing 's' are: $5s, 2s, -4s$

Now, combining the like terms, we get:

$=(10r^2-5r^2)+(-8r-6r)+(5s + 2s -4s)$

$=(10-5)r^2+(-8-6)r+(5+2-4)s$

$=5r^2+(-14)r+3s$

$=5r^2-14r+3s$

Therefore, the final expression is equal to:

$=5r^2-14r+3s$

Now, plug in $r=1,s=3$. This gives,

$=5(1)^2-14(1)+3(3)$

$=5\times 1-14+9$

$=5-14+9$

$=0$

Therefore, the value of the sum of all the terms at $r=1,s=3$ is 0.