Question

simplifique as expressões ​

Answer 1

Resposta:

a) 2x²+6x+5

b) 13x²+10x+2

c) -4x²+17x+9

d) 7x+25

Explicação passo-a-passo:

Devemos ter como base o princípio de que (a+b)²=a²+2ab+b²

a) (x+1)²+(x+2)²

(x²+2•x•1+1²)+(x²+2•x•2+2²)

(x²+2x+1)+(x²+4x+4)

x²+2x+1+x²+4x+4

x²+x²+2x+4x+1+4

2x²+6x+5

b) (2x+1)²+(3x+1)²

[(2x)²+2•2x•1+1²]+[(3x)²+2•3x•1+1²]

(4x²+4x+1)+(9x²+6x+1)

4x²+4x+1+9x²+6x+1

4x²+9x²+4x+6x+1+1

13x²+10x+2

c) 5x-(2x+3)²

5x-[(2x)²+2•2x•3+3²]

5x-(4x²+12x+9)

5x-4x²+12x+9

-4x²+5x+12x+9

-4x²+17x+9

d) (x+5)²-x(x+3)

(x²+2•x•5+5²)-x²-3x

(x²+10x+25)-x²-3x

x²+10x+25-x²-3x

x²-x²+10x-3x+25

7x+25