2. Multiplying Polynomials
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Consider a particular example from Exploration 2. How can you obtain the same result by using the Distributive Property? What can you conclude?
See solution.
As we could see from Exploration 2 with the algebra tiles representation, to multiply two binomials we can multiply each term of one of the binomial factors times each term of the other binomial. Consider, for example, the product (x+3)(x-2).
We can obtain the same result by using the Distributive Property. First, we can distribute (x-2) to each term of (x+3). ( x+ 3)( x-2) = x( x-2) + 3( x-2) Now we can distribute once more and simplify. (x+3)(x-2) &= x(x-2) +3(x-2) (x+3)(x-2) &= x^2-2x +3x-6 (x+3)(x-2) &= x^2+x-6 This method is preferred not only because it saves us the work of drawing the algebra tiles, but it can also be easily extended to any pair of polynomials. We can summarize these ideas as shown below.
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To multiply polynomials, we can use the Distributive Property to distribute one of the factor polynomials to each term of the other polynomial. Then, we can distribute once more and simplify. |