1. Examples of
Incredible Algebra
Techniques

2. DOTS: Difference of Two Squares.
Traditional: a2 – b2 = (a – b)(a + b)
Incredible: a2 – b2 = SS-OM-OP
9x2 – 16
3x SS  Square Root, Square Root
3x – OM  One Minus
3x OP  One Plus
9x2 – 16 = (3x – 4)(3x + 4) SS-OM-OP

3. DOTS: Difference of Two Squares.
Incredible: a2 – b2 = SS-OM-OP
25x2 – 36 =
(5x – 6)(5x + 6)
16x2 – 49 =
(4x – 7)(4x + 7)
64x2 – 81=
(8x – 9)(8x + 9)

4. Square Trinomial Incredible: a2 + 2ab + b2 = SSMAD
Traditional: a2 + 2ab + b2 = (a + b)2
Incredible: a2 + 2ab + b2 = SSMAD
4x2 + 28x + 49
2x SS  Square Root, Square Root
(2x)(7)(2) = 28x MAD  Multiply And Double
2x SS  Square Root, Square Root
( 2x + 7 ) SSMAD (use the middle sign)

5. Square Trinomial Incredible: a2 – 2ab + b2 = SSMAD
Traditional: a2 – 2ab + b2 = (a – b)2
Incredible: a2 – 2ab + b2 = SSMAD
9x2 – 30x + 25
3x SS  Square Root, Square Root
(3x)(5)(2) = 30x MAD  Multiply And Double
3x SS  Square Root, Square Root
( 3x – 5 ) SSMAD (use the middle sign)

6. Square Trinomial Incredible: a2 – 2ab + b2 = SSMAD 16x2 – 72x + 81
4x SS  Square Root, Square Root
(4x)(9)(2) = 72x MAD  Multiply And Double
4x SS  Square Root, Square Root
( 4x – 9 ) SSMAD (use the middle sign)

7. Factoring a Trinomial Incredible: Backwards foil = 36 - 20 36 + x
3x2 – 20x + 12
– 20
1x36
– 2x – 18x
– 2 – 18
2x18
3x2 – 2x – 18x + 12
3x12
x(3x – 2) – 6(3x – 2)
x(3x – 2) (3x – 2)
x(3x – 2)
4x9
(3x – 2)( x – 6)
6x6

8. Singing the Quadratic Formula
X equals negative b,
plus or minus the square root,
Of b squared minus 4 ac
All over 2 a.

9. Polynomial Graph – End Behavior
f(x) = 5x3
f(x) = – 5x3
Leading coefficient is positive so RISES RIGHT.
Leading coefficient is negative so RISES LEFT

10. Polynomial Graph – End Behavior
f(x) = 5x3
Leading coefficient is positive so RISES RIGHT.
Disco Right

11. Polynomial Graph – End Behavior
f(x) = – 5x3
Disco Left
Leading coefficient is negative so RISES LEFT

12. Find the slope of the line joining the points (2, 4) and (5, 3).
Traditional method
Forwards method

13. 1) Find the slope of the line joining the points (3,8) and (-1,2).

14. Find the next point on the line using the slope.
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)
(4, 8)
(x , y)
(9 , 10) x