(3x^6-2x^4)^4

 Esercizio

$\left(3x^6-2x^4\right)^4$

 

Applicare la formula: $\left(a+b\right)^4$$=a^4+4a^3b+6a^2b^2+4ab^3+b^4$, dove $a=3x^6$, $b=-2x^4$ e $a+b=3x^6-2x^4$

$\left(3x^6\right)^4-8\left(3x^6\right)^3x^4+6\left(3x^6\right)^2\left(-2x^4\right)^2+12x^6\left(-2x^4\right)^3+\left(-2x^4\right)^4$

 

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

$81x^{24}-8\cdot 27x^{18}x^4+6\cdot 9x^{12}\left(-2x^4\right)^2+12x^6\left(-2x^4\right)^3+\left(-2x^4\right)^4$

 

Applicare la formula: $ab$$=ab$, dove $ab=-8\cdot 27x^{18}x^4$, $a=-8$ e $b=27$

$81x^{24}-216x^{18}x^4+6\cdot 9x^{12}\left(-2x^4\right)^2+12x^6\left(-2x^4\right)^3+\left(-2x^4\right)^4$

 

Applicare la formula: $ab$$=ab$, dove $ab=6\cdot 9x^{12}\left(-2x^4\right)^2$, $a=6$ e $b=9$

$81x^{24}-216x^{18}x^4+54x^{12}\left(-2x^4\right)^2+12x^6\left(-2x^4\right)^3+\left(-2x^4\right)^4$

 

Applicare la formula: $x^mx^n$$=x^{\left(m+n\right)}$, dove $m=18$ e $n=4$

$81x^{24}-216x^{22}+54x^{12}\left(-2x^4\right)^2+12x^6\left(-2x^4\right)^3+\left(-2x^4\right)^4$

$81x^{24}-216x^{22}+54x^{12}\left(-2x^4\right)^2+12x^6\left(-2x^4\right)^3+\left(-2x^4\right)^4$

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