Esercizio$\left(7x^{2a+1}-4m^{a+2}\right)^3$
Soluzione passo-passo
Passi intermedi
1
Applicare la formula: $\left(a+b\right)^3$$=a^3+3a^2b+3ab^2+b^3$, dove $a=7x^{\left(2a+1\right)}$, $b=-4m^{\left(a+2\right)}$ e $a+b=7x^{\left(2a+1\right)}-4m^{\left(a+2\right)}$
$\left(7x^{\left(2a+1\right)}\right)^3-12\left(7x^{\left(2a+1\right)}\right)^2m^{\left(a+2\right)}+21x^{\left(2a+1\right)}\left(-4m^{\left(a+2\right)}\right)^2+\left(-4m^{\left(a+2\right)}\right)^3$
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Passi intermedi
2
Applicare la formula: $\left(ab\right)^n$$=a^nb^n$
$343x^{3\left(2a+1\right)}-12\cdot 49x^{2\left(2a+1\right)}m^{\left(a+2\right)}+21x^{\left(2a+1\right)}\left(-4m^{\left(a+2\right)}\right)^2+\left(-4m^{\left(a+2\right)}\right)^3$
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3
Applicare la formula: $ab$$=ab$, dove $ab=-12\cdot 49x^{2\left(2a+1\right)}m^{\left(a+2\right)}$, $a=-12$ e $b=49$
$343x^{3\left(2a+1\right)}-588x^{2\left(2a+1\right)}m^{\left(a+2\right)}+21x^{\left(2a+1\right)}\left(-4m^{\left(a+2\right)}\right)^2+\left(-4m^{\left(a+2\right)}\right)^3$
4
Moltiplicare il termine singolo $3$ per ciascun termine del polinomio $\left(2a+1\right)$
$343x^{\left(6a+3\right)}-588x^{2\left(2a+1\right)}m^{\left(a+2\right)}+21x^{\left(2a+1\right)}\left(-4m^{\left(a+2\right)}\right)^2+\left(-4m^{\left(a+2\right)}\right)^3$
5
Moltiplicare il termine singolo $2$ per ciascun termine del polinomio $\left(2a+1\right)$
$343x^{\left(6a+3\right)}-588x^{\left(4a+2\right)}m^{\left(a+2\right)}+21x^{\left(2a+1\right)}\left(-4m^{\left(a+2\right)}\right)^2+\left(-4m^{\left(a+2\right)}\right)^3$
Risposta finale al problema $343x^{\left(6a+3\right)}-588x^{\left(4a+2\right)}m^{\left(a+2\right)}+21x^{\left(2a+1\right)}\left(-4m^{\left(a+2\right)}\right)^2+\left(-4m^{\left(a+2\right)}\right)^3$