Multiply the following two polynomials: (x + 3)(x+3). x + 3 x2x2.

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Presentation transcript:

Multiply the following two polynomials: (x + 3)(x+3). x + 3 x2x2

Multiply the following two polynomials: (x + 3)(x+3). x + 3 x2x2 A perfect square trinomial having the form (a + b) 2 = a2 a2 + 2ab + b2b2

Multiply the following two polynomials: (x - 4)(x - 4). x - 4 x2x2 A perfect square trinomial having the form (a - b) 2 = a2 a2 - 2ab + b2b2

Multiply the following two polynomials: (x - 4)(x - 4). x - 4 x2x2 A perfect square trinomial having the form (a - b) 2 = a 2 - 2ab + b 2

Step 1:1:Factor out the greatest common factor (GCF) if it is larger than 1. Step 2:2:Determine if two of the terms are perfect squares. Step 3:3:Determine if the remaining term is equal to twice the factors of the other two terms. Example:Factor 4x 2 – 20x x 2 is a perfect square. 4x 2 = (2x) is a perfect square. 25 = (5) 2. 2(2x)(5) = 20x. 20x is the middle term. Therefore, 4x 2 – 20x + 25 = (2x – 5) 2.

Determine if the trinomial is a perfect square trinomial. If so, factor the trinomial. 1.x x c 2 – 12c a 2 – 90ac + 81c 2 4.3a a + 48

x x x2 x2 = x  x 100 = 10  2(x)(10) = 20x. This is not a perfect square trinomial since one of the terms is not equal to twice the product of the factors of the terms that are perfect squares.

c2 c2 – 12c + 36 c2 c2 is a perfect square. c2 c2 = c  c 36 is a perfect square. 36 = -6  2(c)(-6) = -12c. This is a perfect square trinomial. c2 c2 – 12c + 36 = (c-6) 2

25a 2 – 90ac + 81c 2 25a 2 is a perfect square. 25a 2 = 5a  81c 2 is a perfect square. 81c 2 = (-9c)  2(5a)(-9c) = -90ac This is a perfect square trinomial. 25a 2 – 90ac + 81c 2 = (5a – 9c) 2

3a a + 48 The GCF for each term is 3. So first, factor out the 3. The first and last terms are perfect squares. a  a = a2a2 4  4 = 16 2(a)(4) = 8a Since the first and last terms are perfect squares and the middle term is equal to twice the product of the factor of the perfect squares, this is a perfect square trinomial.