Question

Simplifique as Expressões.

A) (x+1)^2 + (x+2)^2

B) (2x+1)^2 + (3x+1)^2

C) 5x-(2x+3)^2

D) (x+5)^2 - x(x+3)

Answer 1

Simplifique as Expressões.

A) (x+1)^2 + (x+2)^2

(x + 1)² + (x + 2)² =

(x + 1)(x + 1) + (x + 2)(x + 2)=

(x² + 1x + 1x + 1) + (x² + 2x + 2x + 4) =

(x² + 2x + 1) + (x² + 4x + 4) =

x² + 2x + 1 + x² + 4x + 4 =  junta iguais

x² + x² + 2x + 4x + 1 + 4

2x² + 6x + 5  ( resposta)

 

B) (2x+1)^2 + (3x+1)^2

(2x + 1)² + ( 3x + 1)² =

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

(4x² + 2x + 2x + 1) + (9x² + 3x + 3x + 1) =

(4x² + 4x + 1) + (9x² + 6x + 1) =

4x² + 4x + 1 + 9x² + 6x +  1 =

4x² + 9x² + 4x + 6x + 1 + 1

13x² + 10x + 2 (resposta)

(4x²  

C) 5x-(2x+3)^2

5x - (2x + 3)²

5x - (2x + 3)(2x + 3) =

5x - ( 4x² + 6x + 6x + 9)

5x - (4x² + 12x + 9)  olha o sinal

5x - 4x² - 12x - 9    junta iguais

- 4x² + 5x - 12x - 9

- 4x² - 7x - 9   ( resposta)

D) (x+5)^2 - x(x+3)

(x + 5)² - x(x + 3)

(x + 5)² - x² - 3x

(x + 5)(x + 5) - x² - 3x

(x² + 5x + 5x + 25) - x² - 3x

(x² + 10x + 25) - x² - 3x

x² + 10x + 25 - x² - 3x  junta iguais

x² - x² + 10x - 3x + 25 =

0 + 7x + 25

7x + 25  ( resposta)