1. ALGEBRA I - SECTION 8-7 (Factoring Special Cases)@
SECTION 8-7 : FACTORING SPECIAL CASES

2. (x + 3)(x + 3) (x – 2)(x – 2) (x + 5)2 (x – 6)2 (x + 7)(x – 7)
FOIL the problem associated with your group number.
(x + 3)(x + 3)
(x – 2)(x – 2)
(x + 5)2
(x – 6)2
(x + 7)(x – 7)
(x + 10)(x – 10)
(x – 4)(x + 4)
(x – 11)(x + 11)
x2 + 6x + 9
x2 – 4x + 4
x2 + 10x + 25
x2 – 12x + 36
x2 – 49
x2 – 100
x2 – 16 x

3. SQUARE of a SUM
a2 + 2ab + b2 = (a + b)2
SQUARE of a DIFFERENCE
a2 – 2ab + b2 = (a – b)2
DIFFERENCE of SQUARES
a2 – b2 = (a + b)(a – b)

4. To determine if a trinomial if a square :
NOTE : The 1st and 3rd terms must be positive squares.
Drop the sign of the middle term to the middle of the binomial.
x2 + 8x + 16
( )2 x + 4
Take the square root
of the first term
Take the square root of the third term
Multiply the two terms together. Double the result. If it is the middle term, voila, you have a square.

5. Factor completely. 9) x2 – 10x + 25 11) x2 + 2x + 1 10) 4x2 – 28x + 49
ANSWER : (x – 5)2
ANSWER : (x + 1)2
10) 4x2 – 28x + 49
12) 9m2 + 12m + 4
ANSWER : (2x – 7)2
ANSWER : (3m + 2)2

6. But, can it still be factored?
13) x2 – 5x - 24
But, can it still be factored?
ANSWER : (x – 8)(x + 3)
14) 25x2 + 35x + 9
ANSWER : prime
15) 16z2 – 24z + 9
ANSWER : (4z – 3)2

7. Are these binomials the Difference of Squares? If so, factor.
18) x2 - 64
ANSWER : (a + 5)(a – 5)
ANSWER : (x + 8)(x – 8)
17) y2 - 42
19) 9y2 - 49
ANSWER : not the difference of squares
ANSWER : (3y + 7)(3y – 7)

8. 20) 121 – p2 22) j2 + 25 21) 25p3 – 100p ANSWER : (11 + p)(11 – p) or
ANSWER : you can’t factor the SUM of squares….yet.
21) 25p3 – 100p
ANSWER : 25p(p + 2)(p – 2)