If you multiply (2x + 3) and (x 7) by F-O-I-L method, – a. the product of the first terms is __________. b. the product of the outer terms is __________. c. the product of the inner terms is __________. d. the product of the last terms is __________. e. Do you see any similar terms? What are they? f. What is the result when you combine those similar terms? g. The final answer is _____________. Another Way of Multiplying Polynomials 1. Consider this example. 2. Now, consider this. 7 8 2x + 3 X 5 9 x 7 – 7 0 2 14x + 21 _3 9 0 2x2 + 3x 4 6 0 2 2x2 + 17x + 21 Consider the example below. 3a 5b – 4a + 7 21a 35b – 12a2 20ab – 12a2 20ab + 21a 35b – – D. To multiply a polynomial with more than one term by a polynomial with three or more terms, simply distribute the first term of the first polynomial to each term of the other polynomial. Repeat the procedure up to the last term and simplify the results by combining similar terms. Examples: 1) (x + 3) (x2 2x + 3) = x(x2 2x + 3) 3(x2 2x + 3) – – – – = x3 2x2 + 3x 3x2 + 6x 9 – – – = x3 5x2 + 9x 9 – – 2) (x2 + 3x 4) (4x3 + 5x 1) = x2(4x3 + 5x 1) + 3x(4x3 + 5x 1) - 4(4x3 + – – – – 5x 1) –
If you multiply (2x + 3) and (x – 7) by F-O-I-L method, a. the product of the first terms is __________. b. the product of the outer terms is __________. c. the product of the inner terms is __________. d. the product of the last terms is __________. e. Do you see any similar terms? What are they? f. What is the result when you combine those similar terms? g. The final answer is _____________. Another Way of Multiplying Polynomials 1. Consider this example. 2. Now, consider this. 7 8 2x + 3 X 5 9 x – 7 7 0 2 14x + 21 _3 9 0 2x2 + 3x 4 6 0 2 2x2 + 17x + 21 Consider the example below. 3a – 5b 4a + 7 21a – 35b 12a2 – 20ab 12a2 – 20ab + 21a – 35b D. To multiply a polynomial with more than one term by a polynomial with three or more terms, simply distribute the first term of the first polynomial to each term of the other polynomial. Repeat the procedure up to the last term and simplify the results by combining similar terms. Examples: 1) (x + 3) (x2 – 2x + 3) = x(x2 – 2x + 3) – 3(x2 – 2x + 3) = x3 – 2x2 + 3x – 3x2 + 6x – 9 = x3 – 5x2 + 9x – 9 2) (x2 + 3x – 4) (4x3 + 5x – 1) = x2(4x3 + 5x – 1) + 3x(4x3 + 5x – 1) - 4(4x3 + 5x – 1)
7-math-lm_mod3.docx