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

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

Baholash

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

Yechim qadamlari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(m+n\right)^{2} kengaytirilishi uchun ishlating.

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

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(2m+n\right)^{2} kengaytirilishi uchun ishlating.

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

4m^{2}+4mn+n^{2} teskarisini topish uchun har birining teskarisini toping.

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

-3m^{2} ni olish uchun m^{2} va -4m^{2} ni birlashtirish.

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

-2mn ni olish uchun 2mn va -4mn ni birlashtirish.

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

0 ni olish uchun n^{2} va -n^{2} ni birlashtirish.

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

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(m-9n\right)^{2} kengaytirilishi uchun ishlating.

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

-2m^{2} ni olish uchun -3m^{2} va m^{2} ni birlashtirish.

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

-20mn ni olish uchun -2mn va -18mn ni birlashtirish.

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

Kengaytirish

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

Yechim qadamlari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(m+n\right)^{2} kengaytirilishi uchun ishlating.

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

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(2m+n\right)^{2} kengaytirilishi uchun ishlating.

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

4m^{2}+4mn+n^{2} teskarisini topish uchun har birining teskarisini toping.

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

-3m^{2} ni olish uchun m^{2} va -4m^{2} ni birlashtirish.

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

-2mn ni olish uchun 2mn va -4mn ni birlashtirish.

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

0 ni olish uchun n^{2} va -n^{2} ni birlashtirish.

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

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(m-9n\right)^{2} kengaytirilishi uchun ishlating.

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

-2m^{2} ni olish uchun -3m^{2} va m^{2} ni birlashtirish.

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

-20mn ni olish uchun -2mn va -18mn ni birlashtirish.

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