16. Multiplying a polynomial by a polynomial
Exercises
Multiplying a polynomial by a polynomial
Multiplying a polynomial by a polynomial
Each term of the first factor is multiplied by each term of the second factor. The product is marked by adding the results of each multiplication together.[[$ (a+b)(c+d) = ac +ad + bc+ bd $]]
Note! The terms are multiplied in this order: first, outermost, innermost, and last.
Negligence errors can occur easily when multiplying polynomials,. Remember that each term also has a sign in front of it.
Example 2
Multiply the binomial and the trinomial.
![The + and - signs are determined by the signs of the factors that are multiplied (+2x - 1).](https://peda.net/qis/2022-2023/mathematics/maths-grade-9/oipjp/1pkp/pkp/7:file/photo/3c8a72680f5cab61a1de4f9d497c7617aefb807f/16_example2.png)
Example 1
Determine the area of a rectangle when its side lengths are [[$ 2x +1 $]] and [[$ 3x + 4 $]].
![Example 1.](https://peda.net/qis/2022-2023/mathematics/maths-grade-9/oipjp/1pkp/esimerkki-1/7:file/photo/fb3af1f3cc77d924e6ccf9e1fdb4dd8fc5dcb7d5/16_esimerkki1a_taitto.png)
The area of the rectangle is the sum of the areas of the four smaller rectangles:
[[$ A = 6x^2+8x+3x+4=6x^2+11x+4 $]]On the other hand, the area can also be calculated as the product of the lengths of the rectangle's sides.
![Example 1.](https://peda.net/qis/2022-2023/mathematics/maths-grade-9/oipjp/1pkp/esimerkki-1/72:file/photo/e0a5cdbf8131389d488c21aaa8d5dcb84d6ae4a1/16_esimerkki1b_taitto.png)
Answer: The area of the rectangle is [[$ 6x^2+11x+4 $]].