CDCA – COLÉGIO DIOCESANO CARDEAL ARCOVERDE
ENSINO FUNDAMENTAL II – 7ª SERIE
MATEMÁTICA
PROFESSOR: PEDRO HENRIQUE VALENTIM
Expressões algébricas – Simplificação.
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
2
c – 6c + 9 (c – 3)
c-3
2
10) x2 – 16x + 64 =
(x – 8)2 = x – 8
2
x – 64
(x – 8)(x + 8) x + 8
11)
m2 – 25 = (m – 5)(m + 5) = m - 5
2
m + 10m + 25
(m + 5)2
m+5
12) 4x2 – 4x + 1 = (2x – 1 )2
4x2 – 1
(2x – 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)
PROFESSOR: PEDRO HENRIQUE VALENTIM
MATEMÁTICA
CDCA – COLÉGIO DIOCESANO CARDEAL ARCOVERDE
ENSINO FUNDAMENTAL II – 7ª SERIE
MATEMÁTICA
PROFESSOR: PEDRO HENRIQUE VALENTIM
15) a2 + ab – ac – bc = a.(a + b) – c.(a + b) = (a + b)(a – c) = a + b
a.(a – c)
a.(a – c)
a
a2 – ac
16) 9x2 – 6x + 1 =
(3x – 1)2
= 3x – 1
2
(3x – 1)(3x + 1)
3x + 1
9x – 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
3x. (x – 3)
3x.(x – 3)
x
3x2 – 9x
26) 4x2 + 20x + 25 =
(2x + 5)2
= 2x + 5
2
4x – 25
(2x – 5)(2x + 5)
2x – 5
27) xy2 – 2xy = xy.(y – 2) =
xy
2
y –4
(y – 2)(y +2)
y +2
28) x2 – 4x + 4 = (x – 2)2
xy – 2y
y.(x – 2)
= x–2
y
29) a2 – 2ab + b2 = (a – b)2 = a – b
2a – 2b
2.(a – b)
2
PROFESSOR: PEDRO HENRIQUE VALENTIM
MATEMÁTICA
CDCA – COLÉGIO DIOCESANO CARDEAL ARCOVERDE
ENSINO FUNDAMENTAL II – 7ª SERIE
MATEMÁTICA
PROFESSOR: PEDRO HENRIQUE VALENTIM
30)
= (a – b)(a + b) = a – b
a2 – b2
a + 2ab + b2
(a + b)2
a+b
2
PROFESSOR: PEDRO HENRIQUE VALENTIM
MATEMÁTICA