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Factor a Perfect Square Trinomial High School Algebra Aligned to Common Core State Standards Teacher Notes Insight 360™ is eInstruction’s classroom instruction system that allows you to interact with your students as they learn, quickly gaining insight into student understanding during class so you can adjust instruction in real-time during a single class session. Use this content, designed specifically for use with Insight 360™, to interact with your class. This content includes brief instructional material and two types of activities: Constructed Response Activity for students to complete as an individual or a group assignment. Send each Constructed Response Activity to the Insight 360 iPad Student App. Assessment Item with CueTag™ for students to respond to via student response devices. Receive instant real-time feedback and longitudinal reports. Perfect Square Trinomials Perfect square trinomials are the result of squaring a binomial. (x + 9)2 = (x + 9)(x + 9) = x2 + 9x + 9x + 81 = x2 + 18x + 81 In general terms: (a + b)2 = a2 + ab + ab + b2 = a2 + 2ab + b2 (a – b)2 = a2 – ab – ab + b2 = a2 – 2ab + b2 Expand the following. (5t – 3)2 = (w + 6)2 = (2s – 7)2 = (11x + 8)2 = Expand the following. (5t – 3)2 = 25t2 – 30t +9 (w + 6)2 = w2 + 12w + 36 (2s – 7)2 = 4s2 – 28s + 49 (11x + 8)2 = 121x2 + 176x + 64 Factoring a Perfect Square Trinomial In general terms: (a + b) 2 = a 2 + ab + ab + b2 = a2 + 2ab + b2 (a – b) 2 = a 2 – ab – ab + b2 = a2 – 2ab + b2 In reverse, you would factor a perfect square trinomial like this: a2 + 2ab + b2 = (a + b)2 a2 – 2ab + b2 = (a – b)2 Factoring Steps Factor 49x2 + 28 x + 4 Take the square root of the first term, the sign of the second term, and the square root of the third term. Square the quantity. (7x + 2)2 Check the middle term by multiplying the first term and last term and doubling. [(7x)(2)]2 = 28x This matches the middle term and therefore is the correct factorization. Factor the following. m2 – 10m + 25 = 144p2 – 24p + 1 = 81n2 + 54n + 9 = Factor the following. m2 – 10m + 25 = (m – 5)2 144p2 – 24p + 1 = (12p – 1)2 81n2 + 54n + 9 = (9n + 3)2 Solve using the Zero Product Property. Use the reasons given for each step to guide you. x2 = 3(2x – 3) x2 = 3(2x – 3) Given Distributive Property Addition Property of Equality Addition Property of Equality Distributive Property Zero Product Property Addition Property of Equality Solve using the Zero Product Property. Use the reasons given for each step to guide you. x2 = 3(2x – 3) x2 = 3(2x – 3) Given x2 = 6x – 9 Distributive Property x2 – 6x = - 9 Addition Property of Equality x2 – 6x + 9 = 0 Addition Property of Equality (x – 3)2 = 0 Distributive Property x–3=0 x–3=0 Zero Product Property x=3 x=3 Addition Property of Equality Find the zeros of the function. 4x2 12x + 9 = 0 Solve and graph the solution. 25x2 + 4 = 20x Solve and graph the solution. 25x2 + 4 = 20x 25x2 20x + 4 = 0 (5x 2)2 = 0 5x 2 = 0 5x 2 = 0 5x = 2 5x = 2 x = 2/5 x = 2/5 For information about Insight 360™, visit http://www.einstruction.com. For additional content samples, click here.