Question

1°) Calcule os produtos notáveis*
a) (3 + 4x)²=

b) (2x² - 3y)²=

C) (7a + 6b)²

D) (10 - 5x)²

e) (4 + 7y)(4 - 7y) =

f) (6x⁶ - 8)(6x⁶ + 8) =

g)(15 + 13a⁴)(15 - 13a⁴) =

h)(8x⁹ - 17y⁷)(8x⁹ + 17y⁷)=

2°) fatore as expressões:
a) 9 + 24a +a²=

b) 4a⁴ - 12a²b + 9b²=

c) 49x² + 84xy + 36y²=

d) 100 - 100y² + 25y⁴ =

e) 16 - 49x²=

f) 36a¹² - 64=

g) 225 - 169x⁸=

h) 81a¹⁸ - 144b¹⁴ =​

Answer 1

1°)

a) (3 + 4x)²=9+24x+16x²

b) (2x² - 3y)²=4x⁴-12x²y+9y²

C) (7a + 6b)²=49a²+84ab+36b²

D) (10 - 5x)²=100-100x+25x²

e) (4 + 7y)(4 - 7y) =16-49y²

f) (6x⁶ - 8)(6x⁶ + 8) = $\mathtt{36x^{12}-64}$

g)(15 + 13a⁴)(15 - 13a⁴)=$\mathtt{225-169a^8}$

h)(8x⁹ - 17y⁷)(8x⁹ + 17y⁷)

=$\mathtt{64x^{18}-289y^{14}}$

2°) fatore as expressões:

a) 9 + 24a +a²=(a+12-3√15)(a+12+3√15)

b) 4a⁴ - 12a²b + 9b²=(2a²-3b)²

c) 49x² + 84xy + 36y²=(7x+6y)²

d) 100 - 100y² + 25y⁴ =(10-5y²)²

e) 16 - 49x²=(4-7x)(4+7x)

f) 36a¹² - 64= $\mathtt{(6a^6-8)(6a^6+8)}$

g) 225 - 169x⁸=(15-13x⁴) (15+13x⁴)

h) 81a¹⁸ - 144b¹⁴ = $\mathtt{(9a^9-12b^7)(9a^9+12b^7)}$

Answer 2

Resposta:

Explicação passo-a-passo:

1°) Calcule os produtos notáveis:

a) (3 + 4x)²=

(3 + 4x).(3+4x) = 9 + 2.3.4x + 16x^2

= 9 + 24x + 16x^2

= 16x^2 + 24x + 9

__________

b) (2x² - 3y)²=

4x^4 - 2.2x^2.3y + 9y^2

4x^4 - 12x^2.y + 9y^2

__________________

C) (7a + 6b)²

49a^2 + 2.7a.6b + 36b^2

= 49a^2 + 84ab + 36b^2

________________

D) (10 - 5x)²

= 100 - 2.10.5x + 25x^2

= 100 - 100x + 25x^2

= 25x^2 - 100x + 100

______________

e) (4 + 7y)(4 - 7y) =

= 16 - 49y^2

------------------------

f) (6x⁶ - 8)(6x⁶ + 8) =

= 36x^12 - 64

______________

g)(15 + 13a⁴)(15 - 13a⁴) =

= 225 - 169a^8

______________

h)(8x⁹ - 17y⁷)(8x⁹ + 17y⁷)=

= 64x^ 18 - 289y^14

__________________

2°) fatore as expressões:

a) 9 + 24a +a²=

= a^2 + 24a + 9

3^2 e a^2

a) 9 + 24a + a²

R.: (a+12-3√15).(a+12+3√15)

Prova real:

= a^2 + a.(12 + 3\/15) +a.(12 - 3\/15) + (12-3\/15).(12+3\/15)

= a^2 + 12a + 3a\/15 + 12a - 3a\/15 + 12.12 + 3.12.\/15 - 3.12\/15 - 9.15

= a^2 + 24a + 144 - 135

= a^2 + 24a + 9

-----------------------------------

Outro exemplo:

Para fatorar vou colocar 16 em a^2

Obs.: 9 + 24a + 16a²=

3^2 + 4a^2

(4a + 3).(4a+ 3) = 16a^2 + 2.3.4a + 9

= 16a^2 + 24a + 9

===================

b) 4a⁴ - 12a²b + 9b²=

(2a^2)^2 e (3b)^2

= (2a^2 - 3b).(2a^2 - 3b)

_________________

c) 49x² + 84xy + 36y²=

49x^2 + 42 xy + 42xy + 36y^2

(7x)^2 e (6y)^2

= (7x + 6y).(7x + 6y)

= (7x+6y)²

______________

d) 100 - 100y² + 25y⁴ =

25y^4 - 100y^2 + 100

(5y)^2 e (10)^2

= (5y^2 - 10).(5y^2 - 10)

= (5y^2 - 10)^2

__________________

e) 16 - 49x²

= 4^2 - (7x)^2

= (4 + 7x).(4 - 7x)

_______________

f) 36a¹² - 64=

= (6a^6)^2 - 8^2

= (6a^6 - 8).(6a^6 + 8)

________________

g) 225 - 169x⁸=

= 15^2 - (13x^4)^2

= (15 + 13x^4).(15 - 13x^4)

____________________

h) 81a¹⁸ - 144b¹⁴ =

= (9a^9)^2 - (12b^7)^2

= (9a^9 + 12b^7).(9a^9 - 12b^7)