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OLYNOMIALS

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OLYNOMIALS

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  1. SPECIAL PRODUCTS OF POLYNOMIALS Special Products of Polynomials When you learn how to recognize the special product polynomials quickly and easily, you can solve them a lot faster.  (x-2)(x+2)--- are there any patterns? (x+5)2--- any patterns here? (x-6)2--- how about here? In the first example, you can cancel out the last two number using the equation for a sum and difference pattern: a2 - b2 In the next two examples you can solve easily using the equation for a squared binomial pattern : a2-2ab+b2

  2. Not, let's work out some equations: • 1. Write out the sum and difference pattern: a2-b2 • (x-2)(x+2)= x2-22 • Then you solve the equation: • =x2-4

  3. Then, solve the equation: • =x2+8x+16 • Here is one more square of a binomial equation: • (2x-5)2 • Write out the square of a binomial pattern: a2+2ab+b2 • Substitute the equation numbers into the model equation: • 4x2+2(2x)(-5)+25 • Solve the equation: • =4x2-20x+25 • As long as you follow the model equation for sum and difference patterns, a2-b2, and the model equation for square of a binomial pattern, a2+2ab+b2, it is extremely easy!

  4. Now, Let's solve a squared binomial: • 1. Write out the square of a binomial pattern: a2+2ab+b2 • =(x+4)2 • = x2+2(4)(x)+42

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