(2m-n)^2-169(m+n)^2 eching

$$( 2 m - n ) ^ { 2 } - 169 ( m + n ) ^ { 2 }$$

Baholash

$$3\left(-11m-14n\right)\left(5m+4n\right)$$

Yechim qadamlari

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

$$4m^{2}-4mn+n^{2}-169\left(m+n\right)^{2}$$

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

$$4m^{2}-4mn+n^{2}-169\left(m^{2}+2mn+n^{2}\right)$$

-169 ga m^{2}+2mn+n^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4m^{2}-4mn+n^{2}-169m^{2}-338mn-169n^{2}$$

-165m^{2} ni olish uchun 4m^{2} va -169m^{2} ni birlashtirish.

$$-165m^{2}-4mn+n^{2}-338mn-169n^{2}$$

-342mn ni olish uchun -4mn va -338mn ni birlashtirish.

$$-165m^{2}-342mn+n^{2}-169n^{2}$$

-168n^{2} ni olish uchun n^{2} va -169n^{2} ni birlashtirish.

$$-165m^{2}-342mn-168n^{2}$$

Kengaytirish

$$-165m^{2}-342mn-168n^{2}$$

Yechim qadamlari

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

$$4m^{2}-4mn+n^{2}-169\left(m+n\right)^{2}$$

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

$$4m^{2}-4mn+n^{2}-169\left(m^{2}+2mn+n^{2}\right)$$

-169 ga m^{2}+2mn+n^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4m^{2}-4mn+n^{2}-169m^{2}-338mn-169n^{2}$$

-165m^{2} ni olish uchun 4m^{2} va -169m^{2} ni birlashtirish.

$$-165m^{2}-4mn+n^{2}-338mn-169n^{2}$$

-342mn ni olish uchun -4mn va -338mn ni birlashtirish.

$$-165m^{2}-342mn+n^{2}-169n^{2}$$

-168n^{2} ni olish uchun n^{2} va -169n^{2} ni birlashtirish.

$$-165m^{2}-342mn-168n^{2}$$