Question

(x.y)^4 = x^4.y^4
(x+y)^4 = x^4+y^4
(x-y)^4 = x^4-y^4
(x+y)^0 = 1
diga quais sao verdadeiras e quais são falsas e dê o resultado das falsas.​

Answer 1

Oie, Td Bom?!

I.

>>> Verdadeiro.

$(xy) {}^{4} = x {}^{4} y {}^{4}$

$x {}^{4} y {}^{4} = x {}^{4} y {}^{4}$

II.

>>> Falso.

$(x + y) {}^{4} = x {}^{4} + y {}^{4}$

$(x + y) {}^{2 + 2} = x {}^{4} + y {}^{4}$

$(x + y) {}^{2} .(x + y) {}^{2} = x {}^{4} + y {}^{4}$

$(x {}^{2} + 2xy + y {}^{2} ).(x {}^{2} + 2xy + y {}^{2} ) = x {}^{4} + y {}^{4}$

$x {}^{4} + 2x {}^{3} y + x {}^{2} y {}^{2} + 2x {}^{3} y + 4x {}^{2} y {}^{2} + 2xy {}^{3} + x {}^{2} y {}^{2} + 2xy {}^{3} + y {}^{4} = x {}^{4} + y {}^{4}$

$x {}^{4} + 4x {}^{3} y + 6x {}^{2} y {}^{2} + 4xy {}^{3} + y {}^{4} = x {}^{4} + y {}^{4}$

III.

>>> Falso.

$(x - y) {}^{4} = x {}^{4} - y {}^{4}$

$(x - y) {}^{2 + 2} = x {}^{4} - y {}^{4}$

$(x - y) {}^{2} .(x - y) {}^{2} = x {}^{4} - y {}^{4}$

$(x {}^{2} - 2xy + y {}^{2} ).(x {}^{2} - 2xy + y {}^{2} ) = x {}^{4} - y {}^{4}$

$x {}^{4} - 2x {}^{3} y + x {}^{2} y {}^{2} - 2x {}^{3} y + 4x {}^{2} y {}^{2} - 2xy {}^{3} + x {}^{2} y {}^{2} - 2xy {}^{3} + y {}^{4} = x {}^{4} - y {}^{4}$

$x {}^{4} - 4x {}^{3} y + 6x {}^{2} y {}^{2} - 4xy {}^{3} + y {}^{4} = x {}^{4} - y {}^{4}$

IV.

>>> Verdadeiro.

$(x + y) {}^{0} = 1$

$1 = 1$

Att. Makaveli1996