Question

RESOLVA:
a) (3a+2)²= f) (4x-6y)²=
b) (5a²+1)²= g) (4x³-2y)=
c) (4a+y³)²= h) (a²+bc)²=
d) (3x+5y)²= i) (1 -xy²)²=
e) 1 + 3 ²
    ---- ----
    2     1 
 

Answer 1

RESOLVA:
a) (3a+2)²=

(3a + 2)(3a + 2) =
3a.3a + 3a.2 + 2.3a + 2.2 =
   9a²   + 6a    + 6a   + 4 =
9a² + 12a + 4
assim
(3a + 2)² = 9a² + 12a + 4


 f) (4x-6y)²=

(4x - 6y)(4x - 6y) =
4x.4x - 4x.6y - 6y.4x + 6y6y
  16x²  - 24xy  - 24xy    + 36y²
16x² - 48xy  + 36y²
assim
(4x - 6y)² = 16x² - 48xy + 36y²


b) (5a²+1)²=

(5a² + 1)(5a² +  1) =
5a².5a² + 5a².1 + 1.5a² + 1.1
25a⁴ + 5a² + 5a² + 1 =
25a⁴ + 10a² + 1

assim
(5a² + 1)² = 25a⁴ + 10a² + 1

 g) (4x³-2y)=  ????????
SERÁ qua faltou  (²))

(4x³ - 2y)²
(4x³ - 2y)(4x³ - 2y) =
4x³.4x³ - 4x³.2y - 2y.4x³ + 2y2y
16x⁶      - 8x³y   - 8x³y    + 4y²
16x⁶ - 16x³y + 4y²

assim

(4x³ - 2y)² = 16x⁶ - 16x³y + 4y²

c) (4a+y³)²=


(4a + y³)(4a + y³) =
4a.4a + 4a.y³ + y³.4a + y³y³ =
  16a²    + 4ay³ + 4ay³ + y⁶
16a² + 8ay³+ y⁶

assim
(4a + y³)² = 16a² + 8ay³ + y⁶


 h) (a²+bc)²=

(a² + bc)(a² + bc) =
a².a² + a².bc + bc.a² + bcbc = 
 a⁴    + a²bc   + a²bc   + b²c²
a⁴ + 2a²bc + b²c²

asiim
(a² + bc)² = a⁴ + 2a²bc + b²c²

d) (3x+5y)²=

(3x + 5y)(3x + 5y) =
3x.3x + 3x.5y + 5y.3x + 5y5y
   9x²   + 15xy  + 15xy + 25y²
9x² + 30xy + 25²

assim
(3x + 5y)² = 9x² + 30xy + 25y²

 i)(1 -xy²)²= 

(1 - xy²)(1 - xy²) =
1.1 - 1.xy² - xy².1 + xy²xy²
  1    - xy²  - 1xy² +x²y⁴
1 - 2xy² + x²y⁴

assim
(1 - xy²)² = 1 - 2xy² +  x²y⁴


e)
 
      1 + 3 ²
    ---- ----
    2     1 

1       3²
--- + ------
2       1

1      9
--- + ----
2      1

1 
----- + 9   SOMA com fração faz mmc = 2
2

1(1) + 2(9)         1 + 18           19
---------------- = -----------= ------------
       2                      2                2