Question

Elevar ala cuarta potencia este binomio (xy-2x)

Answer 1

(xy-2x)^4 = [x(y-2)]^4 = x^4 (y-2)^4
               = x^4 [y^4 - 4(y)³(2)+6(y)²(2)² -4(y)(2)³ + (2)^4]
               = x^4 [y^4 - 4(y³)(2)+6(y²)(4) -4(y)(8) + 16]
               = x^4 [y^4 - 8y³+24y² -32y +16]

Answer 2

(xy-2x)⁴
=(xy-2x)²*(xy-2x)²

Resolvamos particularmente:
(xy-2x)²
=(xy-2x)*(xy-2x)
=x²y² -2x*xy - 2x*xy + 4x²
=x²y² - 4x²y +4x²

Ahora:
(x²y² - 4x²y + 4x²)²
=(x²y² - 4x²y + 4x²)*(x²y² - 4x²y +4x²)
=x⁴y⁴ - x²y²*4x²y + x²y²*4x² -4x²y*x²y² + 16x⁴y² + 16x⁴ + 4x²*x²y² -16x⁴y +16x⁴
=x⁴y⁴ - 4x⁴y³ + 4x⁴y² -4x⁴y³ + 16x⁴y² +16x⁴ + 4x⁴y² - 16x⁴y + 16x⁴
=x⁴y⁴ - 8x⁴y³ + 24x⁴y² -16x⁴y + 32x⁴


Saludos.........