From Yahoo Answers

**Question:**

**Answers:**NO ... definitely not. A perfect square is a number whose square root is a whole number (without any decimals). Some examples of perfect squares are: 25 (square root is 5) 36 (square root is 6) 81 (square root is 9) .... I hope you get the concept.

**Question:**Find the value of c that makes each trinomial a perfect square... 1. r^2-9r+c 2. x^2+15x+c

**Answers:**1. r^2 - 9r + c (r - sqrtc)^2 (we now it's subtraction because the middle term is negative and the last term is positive) Let y = sqrtc (r - y)^2 = (r - y)(r - y) = r^2 - 2ry + y^2 r^2 = r^2 -2ry = -9r 2ry = 9r 2y = 9 y = 9/2 sqrtc = y c = y^2 c = (9/2)^2 c = 81/4 2. x^2 + 15x + c (x + sqrtc)^2 (we know it's addition because both the middle and end terms are positive) Let sqrtc = y (x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2 x^2 = x^2 2xy = 15x 2y = 15 y = 15/2 sqrtc = y c = y^2 c = (15/2)^2 c = 225/4

**Question:**I've easily worked through problems like x^2 + xy + y^2, or x^2 -xy + y^2 but what happens when the 3rd term is negative? There are no such examples wherever I look. My problem: 9x^2 + 6xy - 3y^2 I've tried doing things like (3x + y)(3x -2y) but nothing seems to work no matter how close I get. Thanks in advance for your response...

**Answers:**You forgot to pull out the 3 first: 3 ( 3x^2 + 2x y - y^2 ) Now try something like: ( 3x + y ) ( x - y) That's not quite right because: ( 3x + y ) ( x - y) = 3x^2 - 2xy - y^2 So in fact, it is (3x-y)(x+y) So the final answer is: 9x^2 + 6xy - y^2 = 3 (3x-y) (x+y)

From Youtube

### 5-6 Perfect Square Trinomials, Factoring with Mr. Nystrom

perfect squares dude! you can do it! -mr nystrom### Perfect Trinomial Squares (animation) by algebrafree.com, algebra help

Completely free algebra one course in animated video at www.algebrafree.com. Watch all units and use textbook free of charge. Includes chapter reviews and tests. Shows how to recognize a perfect trinomial square and how to factor it, with examples.### College Algebra: Factor Perfect Square Trinomials

www.mindbites.com Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra. This course and others are available from Thinkwell, Inc. The full course can be found atwww.thinkwell.com The full course covers equations and inequalities, relations and functions, polynomial and rational functions, exponential and logarithmic functions, systems of equations, conic sections and a variety of other AP algebra, advanced algebra and Algebra II topics. Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College. He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America". Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences**...**