Multiply the following two polynomials x 3×3 x3

Multiply the following two polynomials: (x + 3)(x+3). x+3 x 2 x+3

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

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

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

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

Determine if the trinomial is a perfect square trinomial. If so, factor the trinomial. 1. x 2 + 10 x + 100 2. c 2 – 12 c + 36 3. 25 a 2 – 90 ac + 81 c 2 4. 3 a 2 + 24 a + 48

x 2 + 10 x + 100 x 2 = x x 100 = 10 2(x)(10) = 20 x. 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.

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

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

3 a 2 + 24 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 = a 2 4 4 = 16 2(a)(4) = 8 a 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.