Lahenda (x-y)^2-8(x^2-y^2)+16(x+y)^2

$$( x - y ) ^ { 2 } - 8 ( x ^ { 2 } - y ^ { 2 } ) + 16 ( x + y ) ^ { 2 }$$

Arvuta

$$\left(3x+5y\right)^{2}$$

Lahenduse etapid

Kasutage kaksliikme \left(x-y\right)^{2} arendamiseks binoomvalemit \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

$$x^{2}-2xy+y^{2}-8\left(x^{2}-y^{2}\right)+16\left(x+y\right)^{2}$$

Kasutage distributiivsusomadust, et korrutada -8 ja x^{2}-y^{2}.

$$x^{2}-2xy+y^{2}-8x^{2}+8y^{2}+16\left(x+y\right)^{2}$$

Kombineerige x^{2} ja -8x^{2}, et leida -7x^{2}.

$$-7x^{2}-2xy+y^{2}+8y^{2}+16\left(x+y\right)^{2}$$

Kombineerige y^{2} ja 8y^{2}, et leida 9y^{2}.

$$-7x^{2}-2xy+9y^{2}+16\left(x+y\right)^{2}$$

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

$$-7x^{2}-2xy+9y^{2}+16\left(x^{2}+2xy+y^{2}\right)$$

Kasutage distributiivsusomadust, et korrutada 16 ja x^{2}+2xy+y^{2}.

$$-7x^{2}-2xy+9y^{2}+16x^{2}+32xy+16y^{2}$$

Kombineerige -7x^{2} ja 16x^{2}, et leida 9x^{2}.

$$9x^{2}-2xy+9y^{2}+32xy+16y^{2}$$

Kombineerige -2xy ja 32xy, et leida 30xy.

$$9x^{2}+30xy+9y^{2}+16y^{2}$$

Kombineerige 9y^{2} ja 16y^{2}, et leida 25y^{2}.

$$9x^{2}+30xy+25y^{2}$$

Laienda

$$9x^{2}+30xy+25y^{2}$$

Lahenduse etapid

Kasutage kaksliikme \left(x-y\right)^{2} arendamiseks binoomvalemit \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

$$x^{2}-2xy+y^{2}-8\left(x^{2}-y^{2}\right)+16\left(x+y\right)^{2}$$

Kasutage distributiivsusomadust, et korrutada -8 ja x^{2}-y^{2}.

$$x^{2}-2xy+y^{2}-8x^{2}+8y^{2}+16\left(x+y\right)^{2}$$

Kombineerige x^{2} ja -8x^{2}, et leida -7x^{2}.

$$-7x^{2}-2xy+y^{2}+8y^{2}+16\left(x+y\right)^{2}$$

Kombineerige y^{2} ja 8y^{2}, et leida 9y^{2}.

$$-7x^{2}-2xy+9y^{2}+16\left(x+y\right)^{2}$$

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

$$-7x^{2}-2xy+9y^{2}+16\left(x^{2}+2xy+y^{2}\right)$$

Kasutage distributiivsusomadust, et korrutada 16 ja x^{2}+2xy+y^{2}.

$$-7x^{2}-2xy+9y^{2}+16x^{2}+32xy+16y^{2}$$

Kombineerige -7x^{2} ja 16x^{2}, et leida 9x^{2}.

$$9x^{2}-2xy+9y^{2}+32xy+16y^{2}$$

Kombineerige -2xy ja 32xy, et leida 30xy.

$$9x^{2}+30xy+9y^{2}+16y^{2}$$

Kombineerige 9y^{2} ja 16y^{2}, et leida 25y^{2}.

$$9x^{2}+30xy+25y^{2}$$