Simplificação de expressões algébricas

Respostas de 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 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)