Respostas

  • Usuário do Brainly
2014-08-21T19:18:24-03:00
A) (x+1)^2+(x+2)^2

Como (a+b)^2=a^2+2ab+b^2, temos:

\rhd (x+1)^2=x^2+2\cdot x\cdot1+1^2=x^2+2x+1;

\rhd (x+2)^2=x^2+2\cdot x\cdot2+2^2=x^2+4x+4;

Assim,

(x+1)^2+(x+2)^2=(x^2+2x+1)+(x^2+4x+4)=2x^2+6x+5.

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

Como antes, temos:

\bullet (2x+1)^2=(2x)^2+2\cdot2x\cdot1+1^2=4x^2+4x+1;

\bullet (3x+1)^2=(3x)^2+2\cdot3x\cdot1+1^2=9x^2+6x+1;

Deste modo,

(2x+1)^2+(3x+1)^2=(4x^2+4x+1)+(9x^2+6x+1)=13x^2+10x+2.

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

Temos que,

(2x+3)^2=(2x)^2+2\cdot2x\cdot3+3^2=4x^2+12x+9

Logo, 5x-(2x+3)^2=5x-(4x^2+12x+9)=-4x^2-7x-9

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

Observe que:

\rhd (x+5)^2=x^2+2\cdot x\cdot5+5^2=x^2+10x+25;

\rhd x(x+3)=x^2+3x

Portanto, (x+5)^2-x(x+3)=(x^2+10x+25)-(x^2+3x)=7x+25.
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