16. Multiplying a polynomial by a polynomial

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 $]]​.