(m+2n)(p+q)=m(p+q)+2n(p+q) eching

$$( m + 2 n ) ( p + q ) = m ( p + q ) + 2 n ( p + q )$$

m uchun yechish (complex solution)

$$m\in \mathrm{C}$$

Yechim qadamlari

m+2n ga p+q ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$mp+mq+2np+2nq=m\left(p+q\right)+2n\left(p+q\right)$$

m ga p+q ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$mp+mq+2np+2nq=mp+mq+2n\left(p+q\right)$$

2n ga p+q ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$mp+mq+2np+2nq=mp+mq+2np+2nq$$

Ikkala tarafdan mp ni ayirish.

$$mp+mq+2np+2nq-mp=mq+2np+2nq$$

0 ni olish uchun mp va -mp ni birlashtirish.

$$mq+2np+2nq=mq+2np+2nq$$

Ikkala tarafdan mq ni ayirish.

$$mq+2np+2nq-mq=2np+2nq$$

0 ni olish uchun mq va -mq ni birlashtirish.

$$2np+2nq=2np+2nq$$

Shartlarni qayta saralash.

$$\text{true}$$

Bu har qanday m uchun to‘g‘ri.

$$m\in \mathrm{C}$$

n uchun yechish (complex solution)

$$n\in \mathrm{C}$$

Yechim qadamlari

m+2n ga p+q ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$mp+mq+2np+2nq=m\left(p+q\right)+2n\left(p+q\right)$$

m ga p+q ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$mp+mq+2np+2nq=mp+mq+2n\left(p+q\right)$$

2n ga p+q ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$mp+mq+2np+2nq=mp+mq+2np+2nq$$

Ikkala tarafdan 2np ni ayirish.

$$mp+mq+2np+2nq-2np=mp+mq+2nq$$

0 ni olish uchun 2np va -2np ni birlashtirish.

$$mp+mq+2nq=mp+mq+2nq$$

Ikkala tarafdan 2nq ni ayirish.

$$mp+mq+2nq-2nq=mp+mq$$

0 ni olish uchun 2nq va -2nq ni birlashtirish.

$$mp+mq=mp+mq$$

Shartlarni qayta saralash.

$$\text{true}$$

Bu har qanday n uchun to‘g‘ri.

$$n\in \mathrm{C}$$

m uchun yechish

$$m\in \mathrm{R}$$

Yechim qadamlari

m+2n ga p+q ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$mp+mq+2np+2nq=m\left(p+q\right)+2n\left(p+q\right)$$

m ga p+q ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$mp+mq+2np+2nq=mp+mq+2n\left(p+q\right)$$

2n ga p+q ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$mp+mq+2np+2nq=mp+mq+2np+2nq$$

Ikkala tarafdan mp ni ayirish.

$$mp+mq+2np+2nq-mp=mq+2np+2nq$$

0 ni olish uchun mp va -mp ni birlashtirish.

$$mq+2np+2nq=mq+2np+2nq$$

Ikkala tarafdan mq ni ayirish.

$$mq+2np+2nq-mq=2np+2nq$$

0 ni olish uchun mq va -mq ni birlashtirish.

$$2np+2nq=2np+2nq$$

Shartlarni qayta saralash.

$$\text{true}$$

Bu har qanday m uchun to‘g‘ri.

$$m\in \mathrm{R}$$

n uchun yechish

$$n\in \mathrm{R}$$

Yechim qadamlari

m+2n ga p+q ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$mp+mq+2np+2nq=m\left(p+q\right)+2n\left(p+q\right)$$

m ga p+q ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$mp+mq+2np+2nq=mp+mq+2n\left(p+q\right)$$

2n ga p+q ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$mp+mq+2np+2nq=mp+mq+2np+2nq$$

Ikkala tarafdan 2np ni ayirish.

$$mp+mq+2np+2nq-2np=mp+mq+2nq$$

0 ni olish uchun 2np va -2np ni birlashtirish.

$$mp+mq+2nq=mp+mq+2nq$$

Ikkala tarafdan 2nq ni ayirish.

$$mp+mq+2nq-2nq=mp+mq$$

0 ni olish uchun 2nq va -2nq ni birlashtirish.

$$mp+mq=mp+mq$$

Shartlarni qayta saralash.

$$\text{true}$$

Bu har qanday n uchun to‘g‘ri.

$$n\in \mathrm{R}$$