Datrys 2(y-3x)^2+2(y+2x)(y-2x)-9x^2-2xy-(2y-x)^2

$$2 ( y - 3 x ) ^ { 2 } + 2 ( y + 2 x ) ( y - 2 x ) - 9 x ^ { 2 } - 2 x y - ( 2 y - x ) ^ { 2 }$$

Enrhifo

$$-10xy$$

Camau Ateb

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(y-3x\right)^{2}.

$$2\left(y^{2}-6yx+9x^{2}\right)+2\left(y+2x\right)\left(y-2x\right)-9x^{2}-2xy-\left(2y-x\right)^{2}$$

Defnyddio’r briodwedd ddosbarthu i luosi 2 â y^{2}-6yx+9x^{2}.

$$2y^{2}-12yx+18x^{2}+2\left(y+2x\right)\left(y-2x\right)-9x^{2}-2xy-\left(2y-x\right)^{2}$$

Defnyddio’r briodwedd ddosbarthu i luosi 2 â y+2x.

$$2y^{2}-12yx+18x^{2}+\left(2y+4x\right)\left(y-2x\right)-9x^{2}-2xy-\left(2y-x\right)^{2}$$

Defnyddio’r briodwedd ddosbarthu i luosi 2y+4x â y-2x a chyfuno termau tebyg.

$$2y^{2}-12yx+18x^{2}+2y^{2}-8x^{2}-9x^{2}-2xy-\left(2y-x\right)^{2}$$

Cyfuno 2y^{2} a 2y^{2} i gael 4y^{2}.

$$4y^{2}-12yx+18x^{2}-8x^{2}-9x^{2}-2xy-\left(2y-x\right)^{2}$$

Cyfuno 18x^{2} a -8x^{2} i gael 10x^{2}.

$$4y^{2}-12yx+10x^{2}-9x^{2}-2xy-\left(2y-x\right)^{2}$$

Cyfuno 10x^{2} a -9x^{2} i gael x^{2}.

$$4y^{2}-12yx+x^{2}-2xy-\left(2y-x\right)^{2}$$

Cyfuno -12yx a -2xy i gael -14yx.

$$4y^{2}-14yx+x^{2}-\left(2y-x\right)^{2}$$

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(2y-x\right)^{2}.

$$4y^{2}-14yx+x^{2}-\left(4y^{2}-4yx+x^{2}\right)$$

I ddod o hyd i wrthwyneb 4y^{2}-4yx+x^{2}, dewch o hyd i wrthwyneb pob term.

$$4y^{2}-14yx+x^{2}-4y^{2}+4yx-x^{2}$$

Cyfuno 4y^{2} a -4y^{2} i gael 0.

$$-14yx+x^{2}+4yx-x^{2}$$

Cyfuno -14yx a 4yx i gael -10yx.

$$-10yx+x^{2}-x^{2}$$

Cyfuno x^{2} a -x^{2} i gael 0.

$$-10yx$$

Ehangu

$$-10xy$$

Camau Ateb

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(y-3x\right)^{2}.

$$2\left(y^{2}-6yx+9x^{2}\right)+2\left(y+2x\right)\left(y-2x\right)-9x^{2}-2xy-\left(2y-x\right)^{2}$$

Defnyddio’r briodwedd ddosbarthu i luosi 2 â y^{2}-6yx+9x^{2}.

$$2y^{2}-12yx+18x^{2}+2\left(y+2x\right)\left(y-2x\right)-9x^{2}-2xy-\left(2y-x\right)^{2}$$

Defnyddio’r briodwedd ddosbarthu i luosi 2 â y+2x.

$$2y^{2}-12yx+18x^{2}+\left(2y+4x\right)\left(y-2x\right)-9x^{2}-2xy-\left(2y-x\right)^{2}$$

Defnyddio’r briodwedd ddosbarthu i luosi 2y+4x â y-2x a chyfuno termau tebyg.

$$2y^{2}-12yx+18x^{2}+2y^{2}-8x^{2}-9x^{2}-2xy-\left(2y-x\right)^{2}$$

Cyfuno 2y^{2} a 2y^{2} i gael 4y^{2}.

$$4y^{2}-12yx+18x^{2}-8x^{2}-9x^{2}-2xy-\left(2y-x\right)^{2}$$

Cyfuno 18x^{2} a -8x^{2} i gael 10x^{2}.

$$4y^{2}-12yx+10x^{2}-9x^{2}-2xy-\left(2y-x\right)^{2}$$

Cyfuno 10x^{2} a -9x^{2} i gael x^{2}.

$$4y^{2}-12yx+x^{2}-2xy-\left(2y-x\right)^{2}$$

Cyfuno -12yx a -2xy i gael -14yx.

$$4y^{2}-14yx+x^{2}-\left(2y-x\right)^{2}$$

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(2y-x\right)^{2}.

$$4y^{2}-14yx+x^{2}-\left(4y^{2}-4yx+x^{2}\right)$$

I ddod o hyd i wrthwyneb 4y^{2}-4yx+x^{2}, dewch o hyd i wrthwyneb pob term.

$$4y^{2}-14yx+x^{2}-4y^{2}+4yx-x^{2}$$

Cyfuno 4y^{2} a -4y^{2} i gael 0.

$$-14yx+x^{2}+4yx-x^{2}$$

Cyfuno -14yx a 4yx i gael -10yx.

$$-10yx+x^{2}-x^{2}$$

Cyfuno x^{2} a -x^{2} i gael 0.

$$-10yx$$