Do Now
Factor completely.
2xy3 – 6xy2 – 36xy
Factor completely.
4v4w – 4v3w – 80v2w
Homework Solutions
7)
2(y2 + 14y + 13)
2(y + 13)(y + 1)
8)
3bc(a2 + 12a + 20)
3bc(a + 10)(a + 2)
Homework Solutions
9)
5c(d2 + 7d + 10)
5c(d + 5)(d + 2)
10) 4mn2(m2 – 2m – 3)
4mn2(m – 3)(m + 1)
Find the Pattern
1
4
9
16
25
36
…
= 12
= 22
= 32
= 42
= 52
= 62
These are perfect squares!
You should be able to list
the first 15 perfect
squares
Perfect squares
1, 4, 9, 16, 25, 36, 49, 64, 81,
100, 121, 144, 169, 196, 225
Find each product.
1) (x + 2) (x – 2)
2) (a + 6) (a – 6)
Can you guess the factored form of
y2 – 49 ?
Difference of Squares
A difference of squares is when
you subtract two perfect squares.
Ex:
x2 – 25
9 – 49y2
a2 – b2 = (a – b)(a + b)
OR
(a + b)(a – b)
1. Factor.
2
x
– 25
2. Factor.
2
c
– 81
3. Factor.
16x2 – 9
4. Factor.
2
25x
–4
5) Factor.
1.
2.
3.
4.
prime
(2m – 8)(2m + 8)
4(-16 + m2)
(m – 4)(m + 4)
Rewrite the problem as
4m2 – 64 so the
subtraction is in the
middle!
-64 +
2
4m
6. Factor.
81a2 – 49b2
7. Factor.
225 – e2
8) Factor.
1.
2.
3.
4.
(x + y)(x + y)
(x – y)(x + y)
(x + y)(x – y)
(x – y)(x – y)
Remember, the order doesn’t matter!
x 2 – y2
9) Factor.
1.
2.
3.
4.
prime
(9c + 4d) (9c – 4d)
(3c – 2d)(3c + 2d)
(3c + 2d)(3c + 2d)
You cannot factor using
difference of squares
because there is no
subtraction!
2
9c
+
2
4d
Homework
Worksheet pg. 547 #’s 1 – 7