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Examples of Incredible Algebra Techniques. DOTS: Difference of Two Squares. Traditional: a 2 – b 2 = (a – b)(a + b). 9x 2 – 16 . 3x 4 SS Square Root, Square Root. 3x – 4 OM One Minus. 3x + 4 OP One Plus. 9x 2 – 16 = (3x – 4)(3x + 4) SS-OM-OP.

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## Examples of Incredible Algebra Techniques

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**Examples of**Incredible Algebra Techniques**DOTS: Difference of Two Squares.**Traditional: a2 – b2 = (a – b)(a + b) 9x2 – 16 3x 4 SS Square Root, Square Root 3x – 4 OM One Minus 3x + 4 OP One Plus 9x2 – 16 = (3x – 4)(3x + 4) SS-OM-OP**DOTS: Difference of Two Squares.**25x2 – 36 = (5x – 6)(5x + 6) 16x2 – 49 = (4x – 7)(4x + 7) 64x2 – 81= (8x – 9)(8x + 9)**Square Trinomial**Traditional: a2 + 2ab + b2 = (a + b)2 4x2 + 28x + 49 2x 7 SS Square Root, Square Root (2x)(7)(2) = 28x MAD Multiply And Double 2x 7 SS Square Root, Square Root ( 2x + 7 )2 SSMAD (use the middle sign)**Square Trinomial**Traditional: a2 – 2ab + b2 = (a – b)2 9x2 – 30x + 25 3x 5 SS Square Root, Square Root (3x)(5)(2) = 30x MAD Multiply And Double 3x 5 SS Square Root, Square Root ( 3x – 5 )2 SSMAD (use the middle sign)**Square Trinomial**16x2 – 72x + 81 4x 9 SS Square Root, Square Root (4x)(9)(2) = 72x MAD Multiply And Double 4x 9 SS Square Root, Square Root ( 4x – 9 )2 SSMAD (use the middle sign)**Factoring a Trinomial**• = 36 3x2 – 20x + 12 – 20 1x36 – 2x – 18x – 2 – 18 2x18 3x2 – 2x – 18x + 12 3x12 x(3x– 2) x(3x– 2) (3x – 2) x(3x– 2) – 6(3x – 2) 4x9 (3x– 2)( x – 6) 6x6**Singing the Quadratic Formula**X equals negative b, plus or minus the square root, Of b squared minus 4 ac All over 2 a.**Polynomial Graph – End Behavior**f(x) = 5x3 f(x) = – 5x3 Leading coefficient is positive so RISES RIGHT. Leading coefficient is negative so RISES LEFT**Polynomial Graph – End Behavior**f(x) = 5x3 Leading coefficient is positive so RISES RIGHT. DiscoRight**Polynomial Graph – End Behavior**f(x) = – 5x3 Leading coefficient is negative so RISES LEFT Disco Left**Find the slope of the line joining the points (2, 4) and**(5, 3). Traditional method Forwards method**2) Find the slope of the line joining the points**(-5,7) and (-3, -8). 1) Find the slope of the line joining the points (3,8) and (-1,2).**This method is used to find a second point on the line if**you know a point and the slope. Find the next point on the line using the slope. y If m = 2 =y rise = 2 = y run = 5 = x From (4, 8) find the next point. 2 5 5 x r I S e run Christine’s Method (x , y) + = 5 (9, 10) (x, y) 2 (4, 8) (x , y) (4, 8) (9 , 10) x

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