(m-5n)(m+5n)+(5n-1)^2 eching

$$( m - 5 n ) ( m + 5 n ) + ( 5 n - 1 ) ^ { 2 }$$

Baholash

$$m^{2}-10n+1$$

Yechim qadamlari

Hisoblang: \left(m-5n\right)\left(m+5n\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$m^{2}-\left(5n\right)^{2}+\left(5n-1\right)^{2}$$

\left(5n\right)^{2} ni kengaytirish.

$$m^{2}-5^{2}n^{2}+\left(5n-1\right)^{2}$$

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

$$m^{2}-25n^{2}+\left(5n-1\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(5n-1\right)^{2} kengaytirilishi uchun ishlating.

$$m^{2}-25n^{2}+25n^{2}-10n+1$$

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

$$m^{2}-10n+1$$

Kengaytirish

$$m^{2}-10n+1$$

Yechim qadamlari

Hisoblang: \left(m-5n\right)\left(m+5n\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$m^{2}-\left(5n\right)^{2}+\left(5n-1\right)^{2}$$

\left(5n\right)^{2} ni kengaytirish.

$$m^{2}-5^{2}n^{2}+\left(5n-1\right)^{2}$$

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

$$m^{2}-25n^{2}+\left(5n-1\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(5n-1\right)^{2} kengaytirilishi uchun ishlating.

$$m^{2}-25n^{2}+25n^{2}-10n+1$$

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

$$m^{2}-10n+1$$