Issolvi (5m-m)^2-(m+n)^2

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

Evalwa

$$\left(3m-n\right)\left(5m+n\right)$$

Passi tas-Soluzzjonijiet

Ikkombina 5m u -m biex tikseb 4m.

$$\left(4m\right)^{2}-\left(m+n\right)^{2}$$

Espandi \left(4m\right)^{2}.

$$4^{2}m^{2}-\left(m+n\right)^{2}$$

Ikkalkula 4 bil-power ta' 2 u tikseb 16.

$$16m^{2}-\left(m+n\right)^{2}$$

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

$$16m^{2}-\left(m^{2}+2mn+n^{2}\right)$$

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

$$16m^{2}-m^{2}-2mn-n^{2}$$

Ikkombina 16m^{2} u -m^{2} biex tikseb 15m^{2}.

$$15m^{2}-2mn-n^{2}$$

Espandi

$$15m^{2}-2mn-n^{2}$$

Passi tas-Soluzzjonijiet

Ikkombina 5m u -m biex tikseb 4m.

$$\left(4m\right)^{2}-\left(m+n\right)^{2}$$

Espandi \left(4m\right)^{2}.

$$4^{2}m^{2}-\left(m+n\right)^{2}$$

Ikkalkula 4 bil-power ta' 2 u tikseb 16.

$$16m^{2}-\left(m+n\right)^{2}$$

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

$$16m^{2}-\left(m^{2}+2mn+n^{2}\right)$$

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

$$16m^{2}-m^{2}-2mn-n^{2}$$

Ikkombina 16m^{2} u -m^{2} biex tikseb 15m^{2}.

$$15m^{2}-2mn-n^{2}$$