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

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

Arvuta

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

Lahenduse etapid

Kombineerige 5m ja -m, et leida 4m.

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

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

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

Arvutage 2 aste 4 ja leidke 16.

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

Kasutage kaksliikme \left(m+n\right)^{2} arendamiseks binoomvalemit \left(a+b\right)^{2}=a^{2}+2ab+b^{2}.

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

Avaldise "m^{2}+2mn+n^{2}" vastandi leidmiseks tuleb leida iga liikme vastand.

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

Kombineerige 16m^{2} ja -m^{2}, et leida 15m^{2}.

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

Laienda

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

Lahenduse etapid

Kombineerige 5m ja -m, et leida 4m.

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

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

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

Arvutage 2 aste 4 ja leidke 16.

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

Kasutage kaksliikme \left(m+n\right)^{2} arendamiseks binoomvalemit \left(a+b\right)^{2}=a^{2}+2ab+b^{2}.

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

Avaldise "m^{2}+2mn+n^{2}" vastandi leidmiseks tuleb leida iga liikme vastand.

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

Kombineerige 16m^{2} ja -m^{2}, et leida 15m^{2}.

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