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

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

Evalwa

$$3\left(x^{2}-y^{2}\right)$$

Passi tas-Soluzzjonijiet

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

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

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

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

Biex issib l-oppost ta' x^{2}+4xy+4y^{2}, sib l-oppost ta' kull terminu.

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

Ikkombina 4x^{2} u -x^{2} biex tikseb 3x^{2}.

$$y^{2}+4yx+3x^{2}-4xy-4y^{2}$$

Ikkombina 4yx u -4xy biex tikseb 0.

$$y^{2}+3x^{2}-4y^{2}$$

Ikkombina y^{2} u -4y^{2} biex tikseb -3y^{2}.

$$-3y^{2}+3x^{2}$$

Espandi

$$3x^{2}-3y^{2}$$

Passi tas-Soluzzjonijiet

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

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

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

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

Biex issib l-oppost ta' x^{2}+4xy+4y^{2}, sib l-oppost ta' kull terminu.

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

Ikkombina 4x^{2} u -x^{2} biex tikseb 3x^{2}.

$$y^{2}+4yx+3x^{2}-4xy-4y^{2}$$

Ikkombina 4yx u -4xy biex tikseb 0.

$$y^{2}+3x^{2}-4y^{2}$$

Ikkombina y^{2} u -4y^{2} biex tikseb -3y^{2}.

$$-3y^{2}+3x^{2}$$