espandere (x^2-z)^4

Soluzione

espandere

(x^{2} - z)^{4}

x^{8} - 4 x^{6} z + 6 x^{4} z^{2} - 4 x^{2} z^{3} + z^{4}

Fasi della soluzione

(x^{2} - z)^{4}

Applicare il teorema binomiale:

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

a = x^{2}, b = - z

= i = 0 \sum 4 (i 4) (x^{2})^{(4 - i)} (- z)^{i}

Espandere la sommatoria

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

Semplificare

\frac{4 !}{0 ! ( 4 - 0 ) !} (x^{2})^{4} (- z)^{0} : x^{8}

Semplificare

\frac{4 !}{1 ! ( 4 - 1 ) !} (x^{2})^{3} (- z)^{1} : - 4 x^{6} z

Semplificare

\frac{4 !}{2 ! ( 4 - 2 ) !} (x^{2})^{2} (- z)^{2} : 6 x^{4} z^{2}

Semplificare

\frac{4 !}{3 ! ( 4 - 3 ) !} (x^{2})^{1} (- z)^{3} : - 4 x^{2} z^{3}

Semplificare

\frac{4 !}{4 ! ( 4 - 4 ) !} (x^{2})^{0} (- z)^{4} : z^{4}

= x^{8} - 4 x^{6} z + 6 x^{4} z^{2} - 4 x^{2} z^{3} + z^{4}

f a c t or 2 x^{2} + 20 x + 42

\frac{23}{16}

s im pl i f y 16 \cdot 5 \frac{7}{8}

s im pl i f y 6 - \frac{7}{2}

s im pl i f y 716