Question

desenvolva algébricamente cada quadrado da soma de dois termos

a)
$(xy + \frac{1}{3} {)}^{2}$
b)
$(x + 5 {)}^{2}$
c)
$( {x}^{5} + 2 {x}^{3} {)}^{2}$
d)
$(6 + x {)}^{2}$
e)
$(2x + xy {)}^{2}$
f)
$( {x}^{2} + 1 {)}^{2}$

Answer 1

A)

= (xy + 1/3)^2
= (xy)^2 + 2.1/3 . x + (1/3)^2
= x^2y^2 + 2x/3 + 1/9

B)

= (x+5)^2
= x^2 + 2.5.x + 5^2
= x^2 + 10x + 25

C)
= (x^5 + 2x^3)^2
= (x^5)^2 + 2.2x^3.x^5 + (2x^3)^2
= x^10 + 4x^8 + 4x^6

D)

= (6+x)^2
= 6^2 + 2.6.x + x^2
= 36 + 12x + x^2
= x^2 + 12x + 36

E)
= (2x +xy)^2
= (2x)^2 + 2.2x.xy + (xy)^2
= 4x^2 + 4x^2.y + x^2.y^2

F)

= (x^2 + 1)^2
= (x^2)^2 + 2.1.x^2 + 1^2
= x^4 + 2x^2 + 1