16. Multiplying a polynomial by a polynomial

Exercises

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Basic exercises
Applied exercises
Challenging exercises

Multiplying a polynomial by a polynomial

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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

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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 $]].

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