Question

Efectúa:
(4x+y)(4x+y)+(4x-y)²+(4x+y)²

Answer 1

Respuesta:

$48x^2+8xy+3y^2$

Explicación paso a paso:

$(4x+y)(4x+y)+(4x-y)^2+(4x+y)^2=\\\\(4x+y)^2+(16x^2-8xy+y^2)+(4x+y)^2=\\\\2(4x+y)^2+16x^2-8xy+y^2=\\\\2(16x^2+8xy+y^2)+16x^2-8xy+y^2=\\\\32x^2+16xy+2y^2+16x^2-8xy+y^2=\\\\\boxed{48x^2+8xy+3y^2}$

Answer 2

Hola! :3

Resolvemos según los binomios al cuadrado:

$(a+b)^{2}=a^{2}+2ab+b^{2}$

$(a-b)^{2}=a^{2}-2ab+b^{2}$

Ahora resolvemos:

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

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

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

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

$2(16x^{2}+8xy+y^{2})+(16x^{2}-8xy+y^{2} )$

$32x^{2} +16xy+y^{2}+16x^{2}-8xy+y^{2}$

Ahora agrupamos términos:

$32x^{2}+16x^{2}+16xy-8xy+y^{2}+y^{2}$

$48x^{2}+8xy+2y^{2}$

El resultado final es $48x^{2}+8xy+2y^{2}$

Espero haberte ayudado :D