Issolvi 4(m+n)^2-4(m+n)(n-2)+(n-2)^2

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

Evalwa

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

Passi tas-Soluzzjonijiet

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

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

Uża l-propjetà distributtiva biex timmultiplika 4 b'm^{2}+2mn+n^{2}.

$$4m^{2}+8mn+4n^{2}-4\left(m+n\right)\left(n-2\right)+\left(n-2\right)^{2}$$

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

$$4m^{2}+8mn+4n^{2}-4\left(m+n\right)\left(n-2\right)+n^{2}-4n+4$$

Uża l-propjetà distributtiva biex timmultiplika -4 b'm+n.

$$4m^{2}+8mn+4n^{2}+\left(-4m-4n\right)\left(n-2\right)+n^{2}-4n+4$$

Uża l-propjetà distributtiva biex timmultiplika -4m-4n b'n-2.

$$4m^{2}+8mn+4n^{2}-4mn+8m-4n^{2}+8n+n^{2}-4n+4$$

Ikkombina 8mn u -4mn biex tikseb 4mn.

$$4m^{2}+4mn+4n^{2}+8m-4n^{2}+8n+n^{2}-4n+4$$

Ikkombina 4n^{2} u -4n^{2} biex tikseb 0.

$$4m^{2}+4mn+8m+8n+n^{2}-4n+4$$

Ikkombina 8n u -4n biex tikseb 4n.

$$4m^{2}+4mn+8m+4n+n^{2}+4$$

Espandi

$$4m^{2}+4mn+8m+n^{2}+4n+4$$

Passi tas-Soluzzjonijiet

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

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

Uża l-propjetà distributtiva biex timmultiplika 4 b'm^{2}+2mn+n^{2}.

$$4m^{2}+8mn+4n^{2}-4\left(m+n\right)\left(n-2\right)+\left(n-2\right)^{2}$$

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

$$4m^{2}+8mn+4n^{2}-4\left(m+n\right)\left(n-2\right)+n^{2}-4n+4$$

Uża l-propjetà distributtiva biex timmultiplika -4 b'm+n.

$$4m^{2}+8mn+4n^{2}+\left(-4m-4n\right)\left(n-2\right)+n^{2}-4n+4$$

Uża l-propjetà distributtiva biex timmultiplika -4m-4n b'n-2.

$$4m^{2}+8mn+4n^{2}-4mn+8m-4n^{2}+8n+n^{2}-4n+4$$

Ikkombina 8mn u -4mn biex tikseb 4mn.

$$4m^{2}+4mn+4n^{2}+8m-4n^{2}+8n+n^{2}-4n+4$$

Ikkombina 4n^{2} u -4n^{2} biex tikseb 0.

$$4m^{2}+4mn+8m+8n+n^{2}-4n+4$$

Ikkombina 8n u -4n biex tikseb 4n.

$$4m^{2}+4mn+8m+4n+n^{2}+4$$