M=(-b+1/2a)^2-(b-b(a-3))-(ab^3-075a^3b):(ab) eching

$$M = ( - b + \frac { 1 } { 2 } a ) ^ { 2 } - ( b - b ( a - 3 ) ) - ( a b ^ { 3 } - 075 a ^ { 3 } b ) : ( a b )$$

M uchun yechish

$$M=\frac{a^{2}-16b}{4}$$

$$a\neq 0\text{ and }b\neq 0$$

Qisqa yechim qadamlari

\left(p+q\right)^{2}=p^{2}+2pq+q^{2} binom teoremasini \left(-b+\frac{1}{2}a\right)^{2} kengaytirilishi uchun ishlating.

$$M=\left(-b\right)^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-\left(b-b\left(a-3\right)\right)-\frac{ab^{3}-0\times 75a^{3}b}{ab}$$

2 daraja ko‘rsatkichini -b ga hisoblang va b^{2} ni qiymatni oling.

$$M=b^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-\left(b-b\left(a-3\right)\right)-\frac{ab^{3}-0\times 75a^{3}b}{ab}$$

b ga a-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$M=b^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-\left(b-\left(ba-3b\right)\right)-\frac{ab^{3}-0\times 75a^{3}b}{ab}$$

ba-3b teskarisini topish uchun har birining teskarisini toping.

$$M=b^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-\left(b-ba+3b\right)-\frac{ab^{3}-0\times 75a^{3}b}{ab}$$

4b ni olish uchun b va 3b ni birlashtirish.

$$M=b^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-\left(4b-ba\right)-\frac{ab^{3}-0\times 75a^{3}b}{ab}$$

4b-ba teskarisini topish uchun har birining teskarisini toping.

$$M=b^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-4b+ba-\frac{ab^{3}-0\times 75a^{3}b}{ab}$$

0 hosil qilish uchun 0 va 75 ni ko'paytirish.

$$M=b^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-4b+ba-\frac{ab^{3}-0a^{3}b}{ab}$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$M=b^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-4b+ba-\frac{ab^{3}-0}{ab}$$

\frac{ab^{3}-0}{ab} ichida hali faktorlanmagan ifodalarni faktorlang.

$$M=b^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-4b+ba-\frac{ab^{3}}{ab}$$

Surat va maxrajdagi ikkala ab ni qisqartiring.

$$M=b^{2}+\left(-b\right)a+\frac{1}{4}a^{2}-4b+ba-b^{2}$$

0 ni olish uchun -ba va ba ni birlashtirish.

$$M=b^{2}+\frac{1}{4}a^{2}-4b-b^{2}$$

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

$$M=\frac{1}{4}a^{2}-4b$$

a uchun yechish (complex solution)

$$a=-2\sqrt{M+4b}$$

$$a=2\sqrt{M+4b}\text{, }M\neq -4b\text{ and }b\neq 0$$

a uchun yechish

$$a=2\sqrt{M+4b}$$

$$a=-2\sqrt{M+4b}\text{, }M>-4b\text{ and }b\neq 0$$