Special factor patterns

2. 1. Write as a Binomial:
(9-w)(9+w)
2. Write each square as a
trinomial:
(6c-1)²
3. Simplify:
(y+4)(y+10)

3. a²-b²  (a+b)(a-b)
(First #)² - (Second #)² =
(sum of 2 squares) x (their
difference)

4. Ex:
9a²-4b²=(3a+2b)(3a-2b)
3a is the square root of 9a² and
2b is the square root of 4b²

5. Ex:
36-25

6. 81-16
***After you factor the number the first time, if there
still is an a²-b² in the subtraction binomial, you have
to factor again until there are no squares left.***

7. a²+(-)2ab+b²  (a+(-)b)²
If the middle number in the equation
equals twice the square root of a
times the square root of b, then you
can factor it.

8. Ex:
a²+2a+1= (a+1)²
a and 1 are the square roots of the first and
last numbers

9. Ex:
u²-6u+9

10. Ex:
b²+12b+4
This trinomial can’t be factored this way
because the middle number does not equal
twice the product of the first and last number.

11. Ex:
121c^4-264c²+144
^4 means to the fourth power****

12. x²+(-)bx+c  (x + factor of b
that adds to c) (x +(-) factor of b
that adds to c)

13. Ex:
x²+8x+15= (x+3) (x+5)
5 and 3 add up to 8, and
are a factor pair of 15.

14. Ex:
x²-10x+24

15. Ex:
y²+20yz+91z²

16. Ex:
x^4-15x²y²-16y^4