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Popolare Algebra >

espandere (4x-3y)^6

Soluzione

espandere

(4 x - 3 y)^{6}

Soluzione

4096 x^{6} - 18432 x^{5} y + 34560 x^{4} y^{2} - 34560 x^{3} y^{3} + 19440 x^{2} y^{4} - 5832 x y^{5} + 729 y^{6}

Fasi della soluzione

(4 x - 3 y)^{6}

Applicare il teorema binomiale:

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

a = 4 x, b = - 3 y

= i = 0 \sum 6 (i 6) (4 x)^{(6 - i)} (- 3 y)^{i}

Espandere la sommatoria

= \frac{6 !}{0 ! ( 6 - 0 ) !} (4 x)^{6} (- 3 y)^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} (4 x)^{5} (- 3 y)^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} (4 x)^{4} (- 3 y)^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} (4 x)^{3} (- 3 y)^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} (4 x)^{2} (- 3 y)^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} (4 x)^{1} (- 3 y)^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} (4 x)^{0} (- 3 y)^{6}

Semplificare

\frac{6 !}{0 ! ( 6 - 0 ) !} (4 x)^{6} (- 3 y)^{0} : 4096 x^{6}

Semplificare

\frac{6 !}{1 ! ( 6 - 1 ) !} (4 x)^{5} (- 3 y)^{1} : - 18432 x^{5} y

Semplificare

\frac{6 !}{2 ! ( 6 - 2 ) !} (4 x)^{4} (- 3 y)^{2} : 34560 x^{4} y^{2}

Semplificare

\frac{6 !}{3 ! ( 6 - 3 ) !} (4 x)^{3} (- 3 y)^{3} : - 34560 x^{3} y^{3}

Semplificare

\frac{6 !}{4 ! ( 6 - 4 ) !} (4 x)^{2} (- 3 y)^{4} : 19440 x^{2} y^{4}

Semplificare

\frac{6 !}{5 ! ( 6 - 5 ) !} (4 x)^{1} (- 3 y)^{5} : - 5832 x y^{5}

Semplificare

\frac{6 !}{6 ! ( 6 - 6 ) !} (4 x)^{0} (- 3 y)^{6} : 729 y^{6}

= 4096 x^{6} - 18432 x^{5} y + 34560 x^{4} y^{2} - 34560 x^{3} y^{3} + 19440 x^{2} y^{4} - 5832 x y^{5} + 729 y^{6}

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