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 $]]
Note! The terms are multiplied in this order: first, outermost, innermost, and last.
Negligence errors can occur easily when multiplying polynomials,. Remember that each term also has a sign in front of it.
Example 2
Multiply the binomial and the trinomial.
Example 1
Determine the area of a rectangle when its side lengths are [[$ 2x +1 $]] and [[$ 3x + 4 $]].
The area of the rectangle is the sum of the areas of the four smaller rectangles:
[[$ A = 6x^2+8x+3x+4=6x^2+11x+4 $]]On the other hand, the area can also be calculated as the product of the lengths of the rectangle's sides.
Answer: The area of the rectangle is [[$ 6x^2+11x+4 $]].