Question

Explique 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)

Help me.. Me ajudem!!

Answer 1

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