Expand and simplify: (5r - 6s + s2) (13r + 3s - 5s2)

I got 65r^2-25rs^2+78rs+18s^2+3s^3+5s^4 but it's wrong?! Please correct me!

5r(13r+3s-5s^2) = 65r^2+15rs-25rs^2

-6s(13r+3s-5s^2) = -78rs-18s^2+30s^3
s^2(13r+3s-5s^2) = 13rs^2+3s^3-5s^4

Add them up to get

65r^2 - 63rs - 12rs^2 - 18s^2 + 33s^3 - 5s^4

To expand and simplify the expression (5r - 6s + s^2) (13r + 3s - 5s^2), you need to multiply each term of the first polynomial by each term of the second polynomial. Let's break it down step-by-step:

Step 1: Multiply the first term of the first polynomial, 5r, by each term of the second polynomial:
(5r) * (13r) = 65r^2
(5r) * (3s) = 15rs
(5r) * (-5s^2) = -25rs^2

Step 2: Multiply the second term of the first polynomial, -6s, by each term of the second polynomial:
(-6s) * (13r) = -78rs
(-6s) * (3s) = -18s^2
(-6s) * (-5s^2) = 30s^3

Step 3: Multiply the third term of the first polynomial, s^2, by each term of the second polynomial:
(s^2) * (13r) = 13rs^2
(s^2) * (3s) = 3s^3
(s^2) * (-5s^2) = -5s^4

Now, let's combine these terms:

65r^2 + 15rs - 25rs^2 - 78rs - 18s^2 + 30s^3 + 13rs^2 + 3s^3 - 5s^4

To simplify further, let's combine like terms:

65r^2 - 25rs^2 + 78rs + 18s^2 + 30s^3 + 13rs^2 + 3s^3 - 5s^4

Combining similar terms:

65r^2 - 12rs^2 + 78rs + 18s^2 + 33s^3 - 5s^4

So, the expanded and simplified form of the expression (5r - 6s + s^2) (13r + 3s - 5s^2) is:
65r^2 - 12rs^2 + 78rs + 18s^2 + 33s^3 - 5s^4

To expand and simplify the expression (5r - 6s + s^2) (13r + 3s - 5s^2), we need to multiply each term in the first expression by each term in the second expression and combine like terms.

First, let's distribute the terms in the first expression to the second expression:

5r * (13r + 3s - 5s^2) = 65r^2 + 15rs - 25rs^2
-6s * (13r + 3s - 5s^2) = -78rs - 18s^2 + 30s^3
s^2 * (13r + 3s - 5s^2) = 13rs^2 + 3s^3 - 5s^4

Next, we can combine like terms by adding or subtracting:

Collect the terms with "r^2":
65r^2

Collect the terms with "rs":
15rs - 78rs = -63rs

Collect the terms with "s^2":
-25rs^2 - 18s^2 + 13rs^2 = -12rs^2 - 18s^2

Collect the terms with "s^3":
30s^3 + 3s^3 = 33s^3

Collect the terms with "s^4":
-5s^4

Combining all these terms, we get:

65r^2 - 63rs - 12rs^2 - 18s^2 + 33s^3 - 5s^4

So, the correct expanded and simplified expression is 65r^2 - 63rs - 12rs^2 - 18s^2 + 33s^3 - 5s^4.

(5r - 6s + s2) (13r + 3s - 5s2)

5r x 13r = 65r^2
5r x 3s = 15rs
5r x -5s^2 = -25rs^2
-6s x 13r = -78rs
-6s x 3s = -18s^2
-6s x -5s^2 = 30s^3
s^2 x 13r = 13rs^2
s^2 x 3s = 3s^3
s^2 x -5s^2 = -5s^4

Combined like terms:

-25rs^2 + 13rs^2 = -12rs^2
-78rs + 15rs = -63rs
30s^3 + 3s^3 = 33s^3

Answer:
-5s^4 + 33s^3 - 12rs^2 - 18s^2 - 63rs + 65r^2