Issolvi (x+2y)^2-(x-y)*(x+2y)

$$( x + 2 y ) ^ { 2 } - ( x - y ) \cdot ( x + 2 y )$$

Evalwa

$$3y\left(x+2y\right)$$

Passi tas-Soluzzjonijiet

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

$$x^{2}+4xy+4y^{2}-\left(x-y\right)\left(x+2y\right)$$

Uża l-propjetà distributtiva biex timmultiplika x-y b'x+2y u kkombina termini simili.

$$x^{2}+4xy+4y^{2}-\left(x^{2}+xy-2y^{2}\right)$$

Biex issib l-oppost ta' x^{2}+xy-2y^{2}, sib l-oppost ta' kull terminu.

$$x^{2}+4xy+4y^{2}-x^{2}-xy+2y^{2}$$

Ikkombina x^{2} u -x^{2} biex tikseb 0.

$$4xy+4y^{2}-xy+2y^{2}$$

Ikkombina 4xy u -xy biex tikseb 3xy.

$$3xy+4y^{2}+2y^{2}$$

Ikkombina 4y^{2} u 2y^{2} biex tikseb 6y^{2}.

$$3xy+6y^{2}$$

Espandi

$$3xy+6y^{2}$$

Passi tas-Soluzzjonijiet

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

$$x^{2}+4xy+4y^{2}-\left(x-y\right)\left(x+2y\right)$$

Uża l-propjetà distributtiva biex timmultiplika x-y b'x+2y u kkombina termini simili.

$$x^{2}+4xy+4y^{2}-\left(x^{2}+xy-2y^{2}\right)$$

Biex issib l-oppost ta' x^{2}+xy-2y^{2}, sib l-oppost ta' kull terminu.

$$x^{2}+4xy+4y^{2}-x^{2}-xy+2y^{2}$$

Ikkombina x^{2} u -x^{2} biex tikseb 0.

$$4xy+4y^{2}-xy+2y^{2}$$

Ikkombina 4xy u -xy biex tikseb 3xy.

$$3xy+4y^{2}+2y^{2}$$

Ikkombina 4y^{2} u 2y^{2} biex tikseb 6y^{2}.

$$3xy+6y^{2}$$