left(x+7right)^2+left(-x^2-6x+7right)^2 eching

$${ \left(x+7 \right) }^{ 2 } + { \left(- { x }^{ 2 } -6x+7 \right) }^{ 2 }$$

Baholash

$$\left(x+7\right)^{2}\left(x^{2}-2x+2\right)$$

Yechim qadamlari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+7\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}+14x+49+\left(-x^{2}-6x+7\right)^{2}$$

-x^{2}-6x+7 kvadratini chiqarish.

$$x^{2}+14x+49+36x^{2}+14\left(-x^{2}\right)-12x\left(-x^{2}\right)-84x+\left(-x^{2}\right)^{2}+49$$

12 hosil qilish uchun -12 va -1 ni ko'paytirish.

$$x^{2}+14x+49+36x^{2}+14\left(-x^{2}\right)+12xx^{2}-84x+\left(-x^{2}\right)^{2}+49$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va 2 ni qo‘shib, 3 ni oling.

$$x^{2}+14x+49+36x^{2}+14\left(-x^{2}\right)+12x^{3}-84x+\left(-x^{2}\right)^{2}+49$$

2 daraja ko‘rsatkichini -x^{2} ga hisoblang va \left(x^{2}\right)^{2} ni qiymatni oling.

$$x^{2}+14x+49+36x^{2}+14\left(-x^{2}\right)+12x^{3}-84x+\left(x^{2}\right)^{2}+49$$

37x^{2} ni olish uchun x^{2} va 36x^{2} ni birlashtirish.

$$37x^{2}+14x+49+14\left(-x^{2}\right)+12x^{3}-84x+\left(x^{2}\right)^{2}+49$$

-70x ni olish uchun 14x va -84x ni birlashtirish.

$$37x^{2}-70x+49+14\left(-x^{2}\right)+12x^{3}+\left(x^{2}\right)^{2}+49$$

98 olish uchun 49 va 49'ni qo'shing.

$$37x^{2}-70x+98+14\left(-x^{2}\right)+12x^{3}+\left(x^{2}\right)^{2}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 2 ni ko‘paytirib, 4 ni oling.

$$37x^{2}-70x+98+14\left(-x^{2}\right)+12x^{3}+x^{4}$$

-14 hosil qilish uchun 14 va -1 ni ko'paytirish.

$$37x^{2}-70x+98-14x^{2}+12x^{3}+x^{4}$$

23x^{2} ni olish uchun 37x^{2} va -14x^{2} ni birlashtirish.

$$23x^{2}-70x+98+12x^{3}+x^{4}$$

Kengaytirish

$$x^{4}+12x^{3}+23x^{2}-70x+98$$

Yechim qadamlari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+7\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}+14x+49+\left(-x^{2}-6x+7\right)^{2}$$

-x^{2}-6x+7 kvadratini chiqarish.

$$x^{2}+14x+49+36x^{2}+14\left(-x^{2}\right)-12x\left(-x^{2}\right)-84x+\left(-x^{2}\right)^{2}+49$$

12 hosil qilish uchun -12 va -1 ni ko'paytirish.

$$x^{2}+14x+49+36x^{2}+14\left(-x^{2}\right)+12xx^{2}-84x+\left(-x^{2}\right)^{2}+49$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va 2 ni qo‘shib, 3 ni oling.

$$x^{2}+14x+49+36x^{2}+14\left(-x^{2}\right)+12x^{3}-84x+\left(-x^{2}\right)^{2}+49$$

2 daraja ko‘rsatkichini -x^{2} ga hisoblang va \left(x^{2}\right)^{2} ni qiymatni oling.

$$x^{2}+14x+49+36x^{2}+14\left(-x^{2}\right)+12x^{3}-84x+\left(x^{2}\right)^{2}+49$$

37x^{2} ni olish uchun x^{2} va 36x^{2} ni birlashtirish.

$$37x^{2}+14x+49+14\left(-x^{2}\right)+12x^{3}-84x+\left(x^{2}\right)^{2}+49$$

-70x ni olish uchun 14x va -84x ni birlashtirish.

$$37x^{2}-70x+49+14\left(-x^{2}\right)+12x^{3}+\left(x^{2}\right)^{2}+49$$

98 olish uchun 49 va 49'ni qo'shing.

$$37x^{2}-70x+98+14\left(-x^{2}\right)+12x^{3}+\left(x^{2}\right)^{2}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 2 ni ko‘paytirib, 4 ni oling.

$$37x^{2}-70x+98+14\left(-x^{2}\right)+12x^{3}+x^{4}$$

-14 hosil qilish uchun 14 va -1 ni ko'paytirish.

$$37x^{2}-70x+98-14x^{2}+12x^{3}+x^{4}$$

23x^{2} ni olish uchun 37x^{2} va -14x^{2} ni birlashtirish.

$$23x^{2}-70x+98+12x^{3}+x^{4}$$