espandere (7x^2-5y^4)^5

Soluzione

espandere

(7 x^{2} - 5 y^{4})^{5}

16807 x^{10} - 60025 x^{8} y^{4} + 85750 x^{6} y^{8} - 61250 x^{4} y^{12} + 21875 x^{2} y^{16} - 3125 y^{20}

Fasi della soluzione

(7 x^{2} - 5 y^{4})^{5}

Applicare il teorema binomiale:

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

a = 7 x^{2}, b = - 5 y^{4}

= i = 0 \sum 5 (i 5) (7 x^{2})^{(5 - i)} (- 5 y^{4})^{i}

Espandere la sommatoria

= \frac{5 !}{0 ! ( 5 - 0 ) !} (7 x^{2})^{5} (- 5 y^{4})^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} (7 x^{2})^{4} (- 5 y^{4})^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} (7 x^{2})^{3} (- 5 y^{4})^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} (7 x^{2})^{2} (- 5 y^{4})^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} (7 x^{2})^{1} (- 5 y^{4})^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} (7 x^{2})^{0} (- 5 y^{4})^{5}

Semplificare

\frac{5 !}{0 ! ( 5 - 0 ) !} (7 x^{2})^{5} (- 5 y^{4})^{0} : 16807 x^{10}

Semplificare

\frac{5 !}{1 ! ( 5 - 1 ) !} (7 x^{2})^{4} (- 5 y^{4})^{1} : - 60025 x^{8} y^{4}

Semplificare

\frac{5 !}{2 ! ( 5 - 2 ) !} (7 x^{2})^{3} (- 5 y^{4})^{2} : 85750 x^{6} y^{8}

Semplificare

\frac{5 !}{3 ! ( 5 - 3 ) !} (7 x^{2})^{2} (- 5 y^{4})^{3} : - 61250 x^{4} y^{12}

Semplificare

\frac{5 !}{4 ! ( 5 - 4 ) !} (7 x^{2})^{1} (- 5 y^{4})^{4} : 21875 x^{2} y^{16}

Semplificare

\frac{5 !}{5 ! ( 5 - 5 ) !} (7 x^{2})^{0} (- 5 y^{4})^{5} : - 3125 y^{20}

= 16807 x^{10} - 60025 x^{8} y^{4} + 85750 x^{6} y^{8} - 61250 x^{4} y^{12} + 21875 x^{2} y^{16} - 3125 y^{20}

s im pl i f y x^{2} \cdot y - y \cdot x^{2}

s im pl i f y (- 7 a^{3} b^{7} c)^{2}

s im pl i f y ((x - 3)^{1})^{3} + ((x - 3^{2})^{1})^{3}

s im pl i f y (5 x^{2})^{- 2} \cdot 5^{3} x^{5}

s im pl i f y (\frac{3 a + 1}{( 4 b )})^{3}