Issolvi 5^2left(m-nright)^2-left(m+nright)^2

$${ 5 }^{ 2 } { \left(m-n \right) }^{ 2 } - { \left(m+n \right) }^{ 2 }$$

Evalwa

$$4\left(2m-3n\right)\left(3m-2n\right)$$

Passi tas-Soluzzjonijiet

Ikkalkula 5 bil-power ta' 2 u tikseb 25.

$$25\left(m-n\right)^{2}-\left(m+n\right)^{2}$$

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

$$25\left(m^{2}-2mn+n^{2}\right)-\left(m+n\right)^{2}$$

Uża l-propjetà distributtiva biex timmultiplika 25 b'm^{2}-2mn+n^{2}.

$$25m^{2}-50mn+25n^{2}-\left(m+n\right)^{2}$$

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

$$25m^{2}-50mn+25n^{2}-\left(m^{2}+2mn+n^{2}\right)$$

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

$$25m^{2}-50mn+25n^{2}-m^{2}-2mn-n^{2}$$

Ikkombina 25m^{2} u -m^{2} biex tikseb 24m^{2}.

$$24m^{2}-50mn+25n^{2}-2mn-n^{2}$$

Ikkombina -50mn u -2mn biex tikseb -52mn.

$$24m^{2}-52mn+25n^{2}-n^{2}$$

Ikkombina 25n^{2} u -n^{2} biex tikseb 24n^{2}.

$$24m^{2}-52mn+24n^{2}$$

Espandi

$$24m^{2}-52mn+24n^{2}$$

Passi tas-Soluzzjonijiet

Ikkalkula 5 bil-power ta' 2 u tikseb 25.

$$25\left(m-n\right)^{2}-\left(m+n\right)^{2}$$

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

$$25\left(m^{2}-2mn+n^{2}\right)-\left(m+n\right)^{2}$$

Uża l-propjetà distributtiva biex timmultiplika 25 b'm^{2}-2mn+n^{2}.

$$25m^{2}-50mn+25n^{2}-\left(m+n\right)^{2}$$

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

$$25m^{2}-50mn+25n^{2}-\left(m^{2}+2mn+n^{2}\right)$$

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

$$25m^{2}-50mn+25n^{2}-m^{2}-2mn-n^{2}$$

Ikkombina 25m^{2} u -m^{2} biex tikseb 24m^{2}.

$$24m^{2}-50mn+25n^{2}-2mn-n^{2}$$

Ikkombina -50mn u -2mn biex tikseb -52mn.

$$24m^{2}-52mn+25n^{2}-n^{2}$$

Ikkombina 25n^{2} u -n^{2} biex tikseb 24n^{2}.

$$24m^{2}-52mn+24n^{2}$$