special factor patterns

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)

a²-b² (a+b)(a-b)

(First #)² - (Second #)² = (sum of 2 squares) x (their

difference)

Ex:9a²-4b²=(3a+2b)(3a-2b)

3a is the square root of 9a² and 2b is the square root of 4b²

Ex:36-25

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.***

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.

Ex: a²+2a+1= (a+1)²

a and 1 are the square roots of the first and last numbers

Ex:u²-6u+9

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.

Ex:121c^4-264c²+144

^4 means to the fourth power****

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

that adds to c)

Ex: x²+8x+15 = (x+3) (x+5)

5 and 3 add up to 8, and are a factor pair of 15.

Ex:x²-10x+24

Ex:y²+20yz+91z²

Ex:x^4-15x²y²-16y^4