MULTIPLICATION OF POLYNOMIALS
(3t
2
- 2t + 7)(2t
3
+ 4t - 3) is a mathematical expression telling us to
multiply each term in the second set of parenthesis by each term in the first parenthesis.
Done in the following way:
3t
2
(2t
3
+ 4t - 3)
- 2t (2t
3
+ 4t - 3)
+ 7 (2t
3
+ 4t - 3) =
6t
2+3
+ 12t
2+1
- 9t
2
- 4t
3+1
- 8t
1+1
+ 6t + 14t
3
+ 28t - 21 =
6t
5
+ 12t
3
- 9t
2
- 4t
4
- 8t
2
+ 6t + 14t
3
+ 28t - 21
The
next
step is to simplify by combining like terms:
6t
5
+ 12t
3
- 9t
2
- 4t
4
- 8t
2
+ 6t + 14t
3
+ 28t - 21 =
6t
5
+ 12t
3
+ 14t
3
- 4t
4
- 8t
2
-9t
2
+ 6t + 28t - 21 =
6t
5
+ 26t
3
- 4t
4
- 17t
2
+34t - 21
Next we want to arrange the terms in descending order:
6t
5
+ 26t
3
- 4t
4
- 17t
2
+34t - 21 =
6t
5
- 4t
4
+ 26t
3
- 17t
2
+34t - 21
The above procedure is used for any polynomial including binomials and monomials. For example try these problems
(4t
2
+ t - 7)(t
3
+ 3t - 2) =
answers
(r
7
+ 3r)(r
4
- r
3
) = r
7
(r
4
- r
3
) + 3r(r
4
- r
3
) =
answer
3t
2
( t
3
- 4t
2
+ 2t - 4) =
answer
return