Simplifique as expressões fatorando o numerador
e o denominador:
1) __x2
– 144____ = (x + 12)(x – 12) = x – 12
x2 + 24x + 144
(x + 12)2 x + 12
2) __x2
+22x + 121 = (x + 11)2 = x + 11
x + 11 x + 11
3) x2 - 100 = ( x – 10)(x
+ 10) = x + 10
x – 10 x – 10
4) x2 + 5x = x.( x + 5)
= x
x + 5 x + 5
5) 4x – 8 = 4.(x
- 2) = 4
x – 2 x – 2
6) 5x + 10 = 5.(x
+ 2) = 1
10x + 20
10.(x + 2) 2
7) a2 –
ab = a.( a – b) = a
a – b a – b
8) x2 +
3x = x.(x + 3) = x
4x + 12
4.(x + 3) 4
9) 7c
– 21 = 7.(c – 3) = 7
c2 – 6c + 9 (c – 3)2 c - 3
10) x2 –
16x + 64 = (x – 8)2 = x – 8
x2 – 64 (x – 8)(x + 8) x + 8
11) m2 – 25 = (m – 5)(m + 5) =
m - 5
m2 + 10m + 25 (m + 5)2 m + 5
12) 4x2
– 4x + 1 = (2x – 1 )2 = 2x – 1
4x2 – 1 (2x – 1)(2x + 1) 2x + 1
13) x2 +
6x + 9 = (x + 3)2 = x + 3
x + 3 x + 3
14) a3 –
ab2 = a.(a2 – b2) = a.(a
– b)(a + b) = a – b
a.( a + b) a.(a + b) a(a + b)
15) a2 +
ab – ac – bc = a.(a + b) – c.(a + b) = (a + b)(a – c) = a
+ b
a2 – ac a.(a – c) a.(a – c) a
16) 9x2
– 6x + 1 = (3x – 1)2 =
3x – 1
9x2 – 1 (3x – 1)(3x + 1) 3x + 1
17) x2 +
5x + ax + 5a = x.(x + 5) + a.( x + 5) = (x + 5)(x + a) = x
+ a
2x + 10 2.(x + 5) 2.( x + 5) 2
18) 7a – 7b + am –
bm = 7(a – b) + m(a – b) = (a
– b)(7 + m) = 7 + m
a2 – 2ab + b2 (a – b)2 (a – b)2 a – b
19) x3 –
x2 + 6x – 6 = x2.(x
– 1) + 6.(x – 1) = (x – 1)(x2
+ 6) = x2 + 6
7x5 – 14x4 + 7x3 7x3.(x2 – 2x
+ 1) 7x3. (x – 1)2 7x3 .(x – 1)
20) 4a2 – 9b2
= (2a – 3b)(2a + 3b) = 2a – 3b
4a2 + 12ab + 9b2 (2a + 3b)2 2a + 3b
21) x2 +
4x + 3 = (x + 1)(x + 3) = x + 1
x2 + 6x + 9 (x + 3)2 x + 3
22) x2 –
6x + 8 = ( x – 2)(x – 4) = x
– 4
x2 – 4 (x – 2)(x + 2) x + 2
23) x2 +
x – 6 = (x – 2)(x + 3) = x + 3
x2 – 4x + 4 (x – 2)2 x – 2
24) x2 –
5x + 4 = (x – 1)(x – 4) = x
– 4
x2 – 2x + 1 (x – 1)2 x - 1
25) 3x2
– 18x + 27 = 3.(x2 – 6x + 9) = 3.(x – 3)2 = x - 3
3x2 – 9x 3x. (x – 3) 3x.(x – 3) x
26) 4x2
+ 20x + 25 = (2x + 5)2 =
2x + 5
4x2 – 25 (2x – 5)(2x + 5) 2x – 5
27) xy2
– 2xy = xy.(y – 2) = xy
y2 – 4 (y – 2)(y +2) y +2
28) x2 – 4x + 4 = (x – 2)2 =
x – 2
xy – 2y y.(x – 2) y
29) a2 –
2ab + b2 = (a – b)2 =
a – b
2a – 2b 2.(a – b) 2
30) a2 – b2 =
(a – b)(a + b) = a – b
a2 + 2ab + b2 (a + b)2 a + b