ASSUNTO: MATEMÁTICA ATIVIDADE: LISTA DE EXERCICIOS DATA:

NOME: N.º SÉRIE 9º NOTA:

I) Desenvolva os produtos notáveis:

Quadrado da soma de dois termos (a + b)2 = a2 + 2. a. b + b2

(3x + y2)2 = (3x)2 + 2. 3x. y2 + (y2)2 = 9x2 + 6xy2 + y4

EXERCICIOS

a) (x + 1)2 = b) (2x + 3)2 =

c) (2x + 3y)2 = d) (5a + x)2 =

e) (2ab + 1)2 = f) (x2 + y2)2 =

g) (a2b + ab2)2 = h) (3a + 2bc)2 =

i) (3x5 + y6)2 = j)

Quadrado da diferença de dois termos (a b)2 = a2 2. a. b + b2

(m – 3)2 = m2 – 2. m. 3 + 32 = m2 – 6m + 9

EXERCICIOS

a) (3a – 1)2 = b) (3m – 5n)2 =

c) (2x – 3y)2 = d) (a2 – b3)2 =

e) (3x3 – y2)2 = f) (5ab – 1)2 =

g) (ab2 – a2b)2 = h) (x2y – xy2)2 =

i) (3x2 – y)2 = j)

Produto da soma pela diferença entre dois termos (a + b).(a b) = a2 – b2

(2x + 3y).(2x – 3y) = 4x2 – 9y2

EXERCICIOS

ESCOLA MONTEIRO LOBATO

a) (7 – x2y).(7 + x2y) = b) (x3 + 1).(x3 – 1) =

c) (mn + 1).(mn – 1) = d) (2ab + c2).(2ab – c2) =

e) (2t + 1).(2t – 1) = f) (x2 + 2y).(x2 – 2y) =

g) (x + 7).(x – 7) = h) (3x – 5).(3x + 5) =

i) (4x + 7y).(4x – 7y) = j) (9a + c4).(9a – c4) =

Produto da forma (x + a).(x + b) x2 + (a + b)x + a. b x2 + Sx + P

(x – 2).(x – 3) = x2 + (2 – 3)x + (2).(3) = x2 – 5x + 6

EXERCICIOS

a) (x + 6).(x + 5) = b) (x – 4).(x + 7) =

c) (x + 3).(x 8) = d) (x + 6).(x – 4) =

e) (x – 2).(x + 9) = f) (x + 9).(x + 8) =

g) (x – 5).(x + 9) = h) (x – 8).(x – 2) =

i) (x + 7).(x 6) = j) (x – 6).(x + 3) =

II) Fatore:

Fator comum ab + ac = a(b + c)

EXERCICIOS

a) mx + my = b) 2a + ab =

c) 2ax + 3bx = d) 10a2 – 20a =

e) 24a2 – 8ax = f) 7a2b + 8ab2 =

g) (a + b)x + (a + b)y = h) a2x2y + a2x2 =

i) 6x3 – 12x2 + 36 = j) 7ab2 + 2ax + a2 =

k) 120ax3 – 100ax2 + 60ax = l) 35x3y2 – 14x2y3 =

Agrupamento ac + bc + ad + bd = c (a + b) + d(a + b) = (a + b)(c + d)

EXERCICIOS

a) ax – ay + bx – by = b) 5ax – 5ay + bx – by =

c) x2 + 5x + ax + 5a = d) 6a2 + 2ab – 3ac – bc =

e) t3 + t2 – 7t – 7 = f) x4 – x3 – 9x + 9 =

g) 2b2 + 2 – b2k – k = h) bx2 – 2by + 5x2 – 10y =

i) a5 + a3 + 2a2 + 2 = j) cx + x + c + 1 =

Diferença entre dois quadrados a2 – b2 = (a + b)(a – b)

EXERCICIOS

a) 81a4 – b6 = b) 4x2 – 1 =

c) x4 – y4 = d) x2y2 – 16a2b2 =

e) = f) b2 =

g) 16x2 – 9y2 = h) 1 – m2n2 =

i) x10 – 100 = j) 49h2 – 81p2 =

Trinômio do quadrado perfeito a2 + 2ab + b2 = (a + b)2 ou a2 – 2ab + b2 = (a – b)2

EXERCICIOS

a) a2 + 2a + 1 = b) 1 – 4x + 4x2 =

c) 9m2 + 6m + 1 = d) 1 – 2y + y2 =

e) x2 – 14x + 49 = f) 25x2 – 10x + 1 =

g) 4x2 – 12xy + 9y2 = h) a6 + 12a3 + 36 =

i) 121x2y2 + 44xy + 4 = j)

Trinômio do 2º grau x2 + (a + b)x + ab = (x + a)(x + b)

EXERCICIOS

a) x2 – 2x – 35 = b) y2 + 8y +12 =

c) x2 – x – 72 = d) b2 + 8b + 15 =

e) y2 + 5y 6 = f) t2 + t 2 =

g) x2 – x – 20 = h) k2 + 15k + 56 =

i) y2 + 9y + 8 = j) x2 – 13x + 42 =

III) Calcule os produtos notáveis:

1) (a + 5)2 = 2) (y + 10)2 =

3) (3a + 4)2 = 4) (x2 + a2)2 =

5) (x + 3)2 = 6) (2x + y)2 =

7) (5 + 3x)2 = 8) =

9) (2x + 3xy)2 = 10) =

11) (a – 1)2 = 12) (3 – 2x)2 =

13) (a – 3)2 = 14) (5 – y)2 =

15) (9 – x)2 = 16) (2a – b)2 =

17) (a2 – x2)2 = 18) (x – 2)2 =

19) = 20) (3a2 – 2b3)2 =

21) (t – 6)2 = 22) (3x – 5)(3x + 5) =

23) = 24) (y – 4)(y + 4) =

25) (2a + b)(2a – b) = 26) (x + 7)(x – 7) =

27) (2x + 2y)(2x – 2y) = 28) =

29) (x – 5)(x + 5) = 30) (2x3 – 1)(2x3 + 1) =

31) (m + 4)(m – 4) = 32) (ab2 + c2)(ab2 – c2) =

33) (x + 3)(x + 4) = 34) =

35) = 36) (y + 8)(y + 9) =

37) (x – 9)(x – 2) = 38) =

39) (a + 1)(a + 2) = 40) (r + 5)(r – 3) =

41) (x + 6)(x + 6) = 42) (3m – 5)(2m – 1) =

43) (p + 10)(p + 10) = 44) (b – 5)(b – 3) =

IV) Identifique os casos de fatoração e fatore as expressões algébricas:

1) 4a + 4b = 2) 10ax – 25ay =

3) 15x3y – 11x2z = 4) 6xy2 – 3x2y + 12x3yz =

5) 6xy + 10ab = 6) 12xy – 18y =

7) mn + my = 8) 28ab – 21ac – 14ad =

9) 3x2 + 2y2x + 4y2 + 6x = 10) ax4 + ax3b + cx + cb =

11) ax + x – 2a – 2 = 12) 6ax – 8abx + 6bx – 8b2x =

13) 2ax2 – bx2 – 50a + 25b = 14) a2 + 5a – b2 + 5b =

15) 3ax + 2ay + 3bx + 2by = 16) 8xz – 8yz – 3x + 3y =

17) ax + bx + ay + by + az + bz = 18) x2 – 3x + 2xy – 6y =

19) 5x + 10y – bx – 2yb = 20) (a + b)2 + 2(a + b) =

21) x10 – 49y6 = 22) 9 – 36a2b2 =

23) 4a2 – 25x2y4 = 24) 100x2y4 – 1 =

25) y2 – 6xy + 9x2 = 26) 9a2 – 6a + 1 =

27) x2 – 12x + 36 = 28) 9a2 – 6ab + b2 =

29) x4 + 12x2 + 36 = 30) =

31) = 32) y2 – 8x + 15 =

33) x2 – 9x + 18 = 34) x2 + 4x – 12 =

35) x2 + 12x + 20 = 36) m2 – 4m + 3 =

37) t2 + 7t – 8 = 38) x2 + 4x – 77 =

39) x2 – 13x + 30 = 40) x2 – 10x + 21 =

V) Desenvolva os produtos notáveis e reduza os termos semelhantes.

a) (x + 7)(x – 7) – x2 + 50 b) (3x + 1)(3x – 1) – 8x2 + 1

c) (2a – 3b)(2a + 3b) + 9b2 + 1 d) (5x – 2)2 + (x – 3)(x – 2)

e) (x – 5)2 – (x – 3)2 – 16 f) (2x + 1)2 – 3x2 + 8

g) (x + 2)2 – (x + 4)2 + 4x + 12 h) (x + 1)(x – 3) + 2(x + 1)

i) (m + n)2 – (2m + n)2 j) (x + y)2 + (x + y)(x – y)

k) 6(a + 2)2 + 2(a – 3)2 + (a – 4)(a + 4) l) (2m2 – 3) – 2(m2 + 1)(m2 – 1)

m) (a2b – 5)(a2b + 5) + 2a(ab – 1) n) (x – 1)2 – (2x – 1)2 + (3x – 1)2