Datrys (m+n)^2-(2m+n)^2+(m-9n)^2

$$( m + n ) ^ { 2 } - ( 2 m + n ) ^ { 2 } + ( m - 9 n ) ^ { 2 }$$

Enrhifo

$$81n^{2}-20mn-2m^{2}$$

Camau Ateb

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

$$m^{2}+2mn+n^{2}-\left(2m+n\right)^{2}+\left(m-9n\right)^{2}$$

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

$$m^{2}+2mn+n^{2}-\left(4m^{2}+4mn+n^{2}\right)+\left(m-9n\right)^{2}$$

I ddod o hyd i wrthwyneb 4m^{2}+4mn+n^{2}, dewch o hyd i wrthwyneb pob term.

$$m^{2}+2mn+n^{2}-4m^{2}-4mn-n^{2}+\left(m-9n\right)^{2}$$

Cyfuno m^{2} a -4m^{2} i gael -3m^{2}.

$$-3m^{2}+2mn+n^{2}-4mn-n^{2}+\left(m-9n\right)^{2}$$

Cyfuno 2mn a -4mn i gael -2mn.

$$-3m^{2}-2mn+n^{2}-n^{2}+\left(m-9n\right)^{2}$$

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

$$-3m^{2}-2mn+\left(m-9n\right)^{2}$$

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(m-9n\right)^{2}.

$$-3m^{2}-2mn+m^{2}-18mn+81n^{2}$$

Cyfuno -3m^{2} a m^{2} i gael -2m^{2}.

$$-2m^{2}-2mn-18mn+81n^{2}$$

Cyfuno -2mn a -18mn i gael -20mn.

$$-2m^{2}-20mn+81n^{2}$$

Ehangu

$$81n^{2}-20mn-2m^{2}$$

Camau Ateb

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

$$m^{2}+2mn+n^{2}-\left(2m+n\right)^{2}+\left(m-9n\right)^{2}$$

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

$$m^{2}+2mn+n^{2}-\left(4m^{2}+4mn+n^{2}\right)+\left(m-9n\right)^{2}$$

I ddod o hyd i wrthwyneb 4m^{2}+4mn+n^{2}, dewch o hyd i wrthwyneb pob term.

$$m^{2}+2mn+n^{2}-4m^{2}-4mn-n^{2}+\left(m-9n\right)^{2}$$

Cyfuno m^{2} a -4m^{2} i gael -3m^{2}.

$$-3m^{2}+2mn+n^{2}-4mn-n^{2}+\left(m-9n\right)^{2}$$

Cyfuno 2mn a -4mn i gael -2mn.

$$-3m^{2}-2mn+n^{2}-n^{2}+\left(m-9n\right)^{2}$$

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

$$-3m^{2}-2mn+\left(m-9n\right)^{2}$$

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(m-9n\right)^{2}.

$$-3m^{2}-2mn+m^{2}-18mn+81n^{2}$$

Cyfuno -3m^{2} a m^{2} i gael -2m^{2}.

$$-2m^{2}-2mn-18mn+81n^{2}$$

Cyfuno -2mn a -18mn i gael -20mn.

$$-2m^{2}-20mn+81n^{2}$$