2 Factoring Perfect Square Trinomials What is a perfect square?If a number is squared the result is a perfect square.Example 22=44 is a perfect square.Other examples:32=9 or 42=169 is a perfect square.16 is a perfect square.
3 Factoring Perfect Square Trinomials Here is a list of the perfect squares for the numbers 1-30.12= = =44122= = =48432= = =52942= = =57652= = =62562= = =67672= = =72982= = =78492= = =841102= = =900
4 Factoring Perfect Square Trinomials When a variable is raised to an even power it is a perfect square.Example: (x)(x)= x2x2 is a perfect square.(x3)(x3)= x6 or (x5)(x5)= x10x6 and x10 are both perfect squares.
5 Factoring Perfect Square Trinomials If a number or a variable is a perfect square the square root of the quantity is the number or variable that was squared to get the perfect square.Example: Square 9.9x9 = 8181 is the perfect square.9 is the square root of 81.Example: Square x3(x3) (x3) = x6 or (x3)2 = x6x6 is the perfect square.x3 is the square root of x6
6 Factoring Perfect Square Trinomials Now we are ready to understand the term- perfect square trinomial.The trinomial that results from squaring a binomial is a perfect square trinomial.Example: (x+7)2 = x2+14x+49x2+14x+49 is a perfect square trinomial.We know that a perfect square trinomial always results when a binomial is squared.The reverse is also true.When we factor a perfect square trinomial the result is always a squared binomial.
7 Factoring Perfect Square Trinomials Here are few examples:Factor: x2+10x+25Result: (x+5)2Check by multiplyingx2+10x+25Factor: x2+2xy+y2(x+y) 2Check by multiplying.x2+2xy+y2
8 Factoring Perfect Square Trinomials Not all trinomials are perfect square trinomials.How do we recognize that a trinomial is a perfect square trinomial.The first and last terms of the trinomial must be perfect squares and must be positive.Example: x2+10x+25What about the middle term? +10xTake the square root of the first term x2 and get x.Take the square root of the last term +25 and get 5.Multiply (5)(x) and double the result. 10x. That is your middle term.Two times the product of the square roots of the first and last terms will give the middle term.
9 Factoring Perfect Square Trinomials Here are some examples of trinomials that are perfect square trinomials.4x2 -20x +252x5(2x- 5)29x2 - 48xy + 64y23x8y(3x-8y)22x3 +20x2y+50xy2Factor out the GCF2x(x2+10xy+25y2)x5y2x(x+5y)2
10 Factoring Perfect Square Trinomials Here are some examples that are not perfect square trinomials.x2+10x-25The last term is not positive.x2+2xy+2y2The 2 in the last term is not a perfect square.4x2-10xy+25y2The square root of the first term is 2x.The square root of the last term 5y.2(2x)(5y)= 20xy20xy = 10xy4x2-16xy+8y2There is a common factor of four.4(x2- 4xy + 2y2)The last term of the trinomial is not a perfect square because the 2 in the last term is not perfect square.To get more help go to the tutorial Practice- Factoring Perfect Square Trinomials