Issolvi (m-2)^3-(m+1)^3-9(m-m^2-1)

$$( m - 2 ) ^ { 3 } - ( m + 1 ) ^ { 3 } - 9 ( m - m ^ { 2 } - 1 )$$

Evalwa

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Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} biex tespandi \left(m-2\right)^{3}.

$$m^{3}-6m^{2}+12m-8-\left(m+1\right)^{3}-9\left(m-m^{2}-1\right)$$

Uża teorema binomjali \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} biex tespandi \left(m+1\right)^{3}.

$$m^{3}-6m^{2}+12m-8-\left(m^{3}+3m^{2}+3m+1\right)-9\left(m-m^{2}-1\right)$$

Biex issib l-oppost ta' m^{3}+3m^{2}+3m+1, sib l-oppost ta' kull terminu.

$$m^{3}-6m^{2}+12m-8-m^{3}-3m^{2}-3m-1-9\left(m-m^{2}-1\right)$$

Ikkombina m^{3} u -m^{3} biex tikseb 0.

$$-6m^{2}+12m-8-3m^{2}-3m-1-9\left(m-m^{2}-1\right)$$

Ikkombina -6m^{2} u -3m^{2} biex tikseb -9m^{2}.

$$-9m^{2}+12m-8-3m-1-9\left(m-m^{2}-1\right)$$

Ikkombina 12m u -3m biex tikseb 9m.

$$-9m^{2}+9m-8-1-9\left(m-m^{2}-1\right)$$

Naqqas 1 minn -8 biex tikseb -9.

$$-9m^{2}+9m-9-9\left(m-m^{2}-1\right)$$

Uża l-propjetà distributtiva biex timmultiplika -9 b'm-m^{2}-1.

$$-9m^{2}+9m-9-9m+9m^{2}+9$$

Ikkombina 9m u -9m biex tikseb 0.

$$-9m^{2}-9+9m^{2}+9$$

Ikkombina -9m^{2} u 9m^{2} biex tikseb 0.

$$-9+9$$

Żid -9 u 9 biex tikseb 0.

$$0$$

Fattur

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