Rešite (x+2y)(2y+x)+(-x-2y)^2+(2x-y)(-2x+y)+2x(x-6y)

$$( x + 2 y ) ( 2 y + x ) + ( - x - 2 y ) ^ { 2 } + ( 2 x - y ) ( - 2 x + y ) + 2 x ( x - 6 y )$$

Ovrednoti

$$7y^{2}$$

Koraki rešitve

Pomnožite x+2y in 2y+x, da dobite \left(x+2y\right)^{2}.

$$\left(x+2y\right)^{2}+\left(-x-2y\right)^{2}+\left(2x-y\right)\left(-2x+y\right)+2x\left(x-6y\right)$$

Uporabite binomski izrek \left(a+b\right)^{2}=a^{2}+2ab+b^{2}, da razširite \left(x+2y\right)^{2}.

$$x^{2}+4xy+4y^{2}+\left(-x-2y\right)^{2}+\left(2x-y\right)\left(-2x+y\right)+2x\left(x-6y\right)$$

Uporabite binomski izrek \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, da razširite \left(-x-2y\right)^{2}.

$$x^{2}+4xy+4y^{2}+\left(-x\right)^{2}-4\left(-x\right)y+4y^{2}+\left(2x-y\right)\left(-2x+y\right)+2x\left(x-6y\right)$$

Izračunajte potenco -x števila 2, da dobite x^{2}.

$$x^{2}+4xy+4y^{2}+x^{2}-4\left(-x\right)y+4y^{2}+\left(2x-y\right)\left(-2x+y\right)+2x\left(x-6y\right)$$

Pomnožite -4 in -1, da dobite 4.

$$x^{2}+4xy+4y^{2}+x^{2}+4xy+4y^{2}+\left(2x-y\right)\left(-2x+y\right)+2x\left(x-6y\right)$$

Združite x^{2} in x^{2}, da dobite 2x^{2}.

$$2x^{2}+4xy+4y^{2}+4xy+4y^{2}+\left(2x-y\right)\left(-2x+y\right)+2x\left(x-6y\right)$$

Združite 4xy in 4xy, da dobite 8xy.

$$2x^{2}+8xy+4y^{2}+4y^{2}+\left(2x-y\right)\left(-2x+y\right)+2x\left(x-6y\right)$$

Združite 4y^{2} in 4y^{2}, da dobite 8y^{2}.

$$2x^{2}+8xy+8y^{2}+\left(2x-y\right)\left(-2x+y\right)+2x\left(x-6y\right)$$

Uporabite lastnost distributivnosti za množenje 2x-y krat -2x+y in kombiniranje pogojev podobnosti.

$$2x^{2}+8xy+8y^{2}-4x^{2}+4xy-y^{2}+2x\left(x-6y\right)$$

Združite 2x^{2} in -4x^{2}, da dobite -2x^{2}.

$$-2x^{2}+8xy+8y^{2}+4xy-y^{2}+2x\left(x-6y\right)$$

Združite 8xy in 4xy, da dobite 12xy.

$$-2x^{2}+12xy+8y^{2}-y^{2}+2x\left(x-6y\right)$$

Združite 8y^{2} in -y^{2}, da dobite 7y^{2}.

$$-2x^{2}+12xy+7y^{2}+2x\left(x-6y\right)$$

Uporabite distributivnost, da pomnožite 2x s/z x-6y.

$$-2x^{2}+12xy+7y^{2}+2x^{2}-12xy$$

Združite -2x^{2} in 2x^{2}, da dobite 0.

$$12xy+7y^{2}-12xy$$

Združite 12xy in -12xy, da dobite 0.

$$7y^{2}$$

Razširi

$$7y^{2}$$

Koraki rešitve

Pomnožite x+2y in 2y+x, da dobite \left(x+2y\right)^{2}.

$$\left(x+2y\right)^{2}+\left(-x-2y\right)^{2}+\left(2x-y\right)\left(-2x+y\right)+2x\left(x-6y\right)$$

Uporabite binomski izrek \left(a+b\right)^{2}=a^{2}+2ab+b^{2}, da razširite \left(x+2y\right)^{2}.

$$x^{2}+4xy+4y^{2}+\left(-x-2y\right)^{2}+\left(2x-y\right)\left(-2x+y\right)+2x\left(x-6y\right)$$

Uporabite binomski izrek \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, da razširite \left(-x-2y\right)^{2}.

$$x^{2}+4xy+4y^{2}+\left(-x\right)^{2}-4\left(-x\right)y+4y^{2}+\left(2x-y\right)\left(-2x+y\right)+2x\left(x-6y\right)$$

Izračunajte potenco -x števila 2, da dobite x^{2}.

$$x^{2}+4xy+4y^{2}+x^{2}-4\left(-x\right)y+4y^{2}+\left(2x-y\right)\left(-2x+y\right)+2x\left(x-6y\right)$$

Pomnožite -4 in -1, da dobite 4.

$$x^{2}+4xy+4y^{2}+x^{2}+4xy+4y^{2}+\left(2x-y\right)\left(-2x+y\right)+2x\left(x-6y\right)$$

Združite x^{2} in x^{2}, da dobite 2x^{2}.

$$2x^{2}+4xy+4y^{2}+4xy+4y^{2}+\left(2x-y\right)\left(-2x+y\right)+2x\left(x-6y\right)$$

Združite 4xy in 4xy, da dobite 8xy.

$$2x^{2}+8xy+4y^{2}+4y^{2}+\left(2x-y\right)\left(-2x+y\right)+2x\left(x-6y\right)$$

Združite 4y^{2} in 4y^{2}, da dobite 8y^{2}.

$$2x^{2}+8xy+8y^{2}+\left(2x-y\right)\left(-2x+y\right)+2x\left(x-6y\right)$$

Uporabite lastnost distributivnosti za množenje 2x-y krat -2x+y in kombiniranje pogojev podobnosti.

$$2x^{2}+8xy+8y^{2}-4x^{2}+4xy-y^{2}+2x\left(x-6y\right)$$

Združite 2x^{2} in -4x^{2}, da dobite -2x^{2}.

$$-2x^{2}+8xy+8y^{2}+4xy-y^{2}+2x\left(x-6y\right)$$

Združite 8xy in 4xy, da dobite 12xy.

$$-2x^{2}+12xy+8y^{2}-y^{2}+2x\left(x-6y\right)$$

Združite 8y^{2} in -y^{2}, da dobite 7y^{2}.

$$-2x^{2}+12xy+7y^{2}+2x\left(x-6y\right)$$

Uporabite distributivnost, da pomnožite 2x s/z x-6y.

$$-2x^{2}+12xy+7y^{2}+2x^{2}-12xy$$

Združite -2x^{2} in 2x^{2}, da dobite 0.

$$12xy+7y^{2}-12xy$$

Združite 12xy in -12xy, da dobite 0.

$$7y^{2}$$