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Popular Álgebra >

desarrollar (7z^3-xy)^4-9

Solución

desarrollar

(7 z^{3} - x y)^{4} - 9

Solución

2401 z^{12} - 1372 z^{9} x y + 294 z^{6} x^{2} y^{2} - 28 z^{3} x^{3} y^{3} + x^{4} y^{4} - 9

Pasos de solución

(7 z^{3} - x y)^{4} - 9

Aplicar el teorema del binomio:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 7 z^{3}, b = - x y

= i = 0 \sum 4 (i 4) (7 z^{3})^{(4 - i)} (- x y)^{i}

Expandir sumatorio

= \frac{4 !}{0 ! ( 4 - 0 ) !} (7 z^{3})^{4} (- x y)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (7 z^{3})^{3} (- x y)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (7 z^{3})^{2} (- x y)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (7 z^{3})^{1} (- x y)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (7 z^{3})^{0} (- x y)^{4} - 9

Simplificar

\frac{4 !}{0 ! ( 4 - 0 ) !} (7 z^{3})^{4} (- x y)^{0} : 2401 z^{12}

Simplificar

\frac{4 !}{1 ! ( 4 - 1 ) !} (7 z^{3})^{3} (- x y)^{1} : - 1372 z^{9} x y

Simplificar

\frac{4 !}{2 ! ( 4 - 2 ) !} (7 z^{3})^{2} (- x y)^{2} : 294 z^{6} x^{2} y^{2}

Simplificar

\frac{4 !}{3 ! ( 4 - 3 ) !} (7 z^{3})^{1} (- x y)^{3} : - 28 z^{3} x^{3} y^{3}

Simplificar

\frac{4 !}{4 ! ( 4 - 4 ) !} (7 z^{3})^{0} (- x y)^{4} : x^{4} y^{4}

= 2401 z^{12} - 1372 z^{9} x y + 294 z^{6} x^{2} y^{2} - 28 z^{3} x^{3} y^{3} + x^{4} y^{4} - 9

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