(6xy-1/2pq)^3

 Esercizio

$\left(6xy-\frac{1}{2}pq\right)^3$

 

Applicare la formula: $\left(a+b\right)^3$$=a^3+3a^2b+3ab^2+b^3$, dove $a=6xy$, $b=-\frac{1}{2}pq$ e $a+b=6xy-\frac{1}{2}pq$

$\left(6xy\right)^3-\frac{3}{2}\left(6xy\right)^2pq+18xy\left(-\frac{1}{2}pq\right)^2+\left(-\frac{1}{2}pq\right)^3$

 

Applicare la formula: $\left(ab\right)^n$$=a^nb^n$, dove $a=p$, $b=\left(-\frac{1}{2}\right)q$ e $n=2$

$216x^3y^3+36\left(-\frac{3}{2}\right)x^2y^2pq+18xyp^2\left(-\frac{1}{2}q\right)^2+\left(-\frac{1}{2}pq\right)^3$

 

Applicare la formula: $\left(ab\right)^n$$=a^nb^n$

$216x^3y^3+36\left(-\frac{3}{2}\right)x^2y^2pq+18xyp^2\left(-\frac{1}{2}q\right)^2+p^3\left(\left(-\frac{1}{2}\right)q\right)^3$

 

Applicare la formula: $\frac{a}{b}c$$=\frac{ca}{b}$, dove $a=-3$, $b=2$, $c=36$, $a/b=-\frac{3}{2}$ e $ca/b=36\left(-\frac{3}{2}\right)x^2y^2pq$

$216x^3y^3-54x^2y^2pq+18xyp^2\left(-\frac{1}{2}q\right)^2+p^3\left(\left(-\frac{1}{2}\right)q\right)^3$

$216x^3y^3-54x^2y^2pq+18xyp^2\left(-\frac{1}{2}q\right)^2+p^3\left(\left(-\frac{1}{2}\right)q\right)^3$

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