Issolvi 2(2a+3)^3-3(a-2)^3

$$2 ( 2 a + 3 ) ^ { 3 } - 3 ( a - 2 ) ^ { 3 }$$

Espandi

$$13a^{3}+90a^{2}+72a+78$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(p+q\right)^{3}=p^{3}+3p^{2}q+3pq^{2}+q^{3} biex tespandi \left(2a+3\right)^{3}.

$$2\left(8a^{3}+36a^{2}+54a+27\right)-3\left(a-2\right)^{3}$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'8a^{3}+36a^{2}+54a+27.

$$16a^{3}+72a^{2}+108a+54-3\left(a-2\right)^{3}$$

Uża teorema binomjali \left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} biex tespandi \left(a-2\right)^{3}.

$$16a^{3}+72a^{2}+108a+54-3\left(a^{3}-6a^{2}+12a-8\right)$$

Uża l-propjetà distributtiva biex timmultiplika -3 b'a^{3}-6a^{2}+12a-8.

$$16a^{3}+72a^{2}+108a+54-3a^{3}+18a^{2}-36a+24$$

Ikkombina 16a^{3} u -3a^{3} biex tikseb 13a^{3}.

$$13a^{3}+72a^{2}+108a+54+18a^{2}-36a+24$$

Ikkombina 72a^{2} u 18a^{2} biex tikseb 90a^{2}.

$$13a^{3}+90a^{2}+108a+54-36a+24$$

Ikkombina 108a u -36a biex tikseb 72a.

$$13a^{3}+90a^{2}+72a+54+24$$

Żid 54 u 24 biex tikseb 78.

$$13a^{3}+90a^{2}+72a+78$$

Evalwa

$$2\left(2a+3\right)^{3}-3\left(a-2\right)^{3}$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(p+q\right)^{3}=p^{3}+3p^{2}q+3pq^{2}+q^{3} biex tespandi \left(2a+3\right)^{3}.

$$2\left(8a^{3}+36a^{2}+54a+27\right)-3\left(a-2\right)^{3}$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'8a^{3}+36a^{2}+54a+27.

$$16a^{3}+72a^{2}+108a+54-3\left(a-2\right)^{3}$$

Uża teorema binomjali \left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} biex tespandi \left(a-2\right)^{3}.

$$16a^{3}+72a^{2}+108a+54-3\left(a^{3}-6a^{2}+12a-8\right)$$

Uża l-propjetà distributtiva biex timmultiplika -3 b'a^{3}-6a^{2}+12a-8.

$$16a^{3}+72a^{2}+108a+54-3a^{3}+18a^{2}-36a+24$$

Ikkombina 16a^{3} u -3a^{3} biex tikseb 13a^{3}.

$$13a^{3}+72a^{2}+108a+54+18a^{2}-36a+24$$

Ikkombina 72a^{2} u 18a^{2} biex tikseb 90a^{2}.

$$13a^{3}+90a^{2}+108a+54-36a+24$$

Ikkombina 108a u -36a biex tikseb 72a.

$$13a^{3}+90a^{2}+72a+54+24$$

Żid 54 u 24 biex tikseb 78.

$$13a^{3}+90a^{2}+72a+78$$