5^2left(m-nright)^2-left(m+nright)^2 eching

$${ 5 }^{ 2 } { \left(m-n \right) }^{ 2 } - { \left(m+n \right) }^{ 2 }$$

Baholash

$$4\left(2m-3n\right)\left(3m-2n\right)$$

Yechim qadamlari

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$25\left(m-n\right)^{2}-\left(m+n\right)^{2}$$

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

$$25\left(m^{2}-2mn+n^{2}\right)-\left(m+n\right)^{2}$$

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

$$25m^{2}-50mn+25n^{2}-\left(m+n\right)^{2}$$

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

$$25m^{2}-50mn+25n^{2}-\left(m^{2}+2mn+n^{2}\right)$$

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

$$25m^{2}-50mn+25n^{2}-m^{2}-2mn-n^{2}$$

24m^{2} ni olish uchun 25m^{2} va -m^{2} ni birlashtirish.

$$24m^{2}-50mn+25n^{2}-2mn-n^{2}$$

-52mn ni olish uchun -50mn va -2mn ni birlashtirish.

$$24m^{2}-52mn+25n^{2}-n^{2}$$

24n^{2} ni olish uchun 25n^{2} va -n^{2} ni birlashtirish.

$$24m^{2}-52mn+24n^{2}$$

Kengaytirish

$$24m^{2}-52mn+24n^{2}$$

Yechim qadamlari

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$25\left(m-n\right)^{2}-\left(m+n\right)^{2}$$

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

$$25\left(m^{2}-2mn+n^{2}\right)-\left(m+n\right)^{2}$$

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

$$25m^{2}-50mn+25n^{2}-\left(m+n\right)^{2}$$

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

$$25m^{2}-50mn+25n^{2}-\left(m^{2}+2mn+n^{2}\right)$$

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

$$25m^{2}-50mn+25n^{2}-m^{2}-2mn-n^{2}$$

24m^{2} ni olish uchun 25m^{2} va -m^{2} ni birlashtirish.

$$24m^{2}-50mn+25n^{2}-2mn-n^{2}$$

-52mn ni olish uchun -50mn va -2mn ni birlashtirish.

$$24m^{2}-52mn+25n^{2}-n^{2}$$

24n^{2} ni olish uchun 25n^{2} va -n^{2} ni birlashtirish.

$$24m^{2}-52mn+24n^{2}$$