45s^2-120s+80 eching

$$45 s ^ { 2 } - 120 s + 80$$

Omil

$$5\left(3s-4\right)^{2}$$

Yechim qadamlari

5 omili.

$$5\left(9s^{2}-24s+16\right)$$

Hisoblang: 9s^{2}-24s+16. Kvadrat formuladan foydalaning, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, bu yerda a=3s va b=4.

$$\left(3s-4\right)^{2}$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$5\left(3s-4\right)^{2}$$

Binom kvadrati qadamlari

Ushbu trinomial qiymati trinomial kvadratiga ega, balki umumiy omilga ko'paytirilgan. Trinomial kvadratlar old va oxirgi shartlarning kvadrat ildizini topib omili yechilishi mumkin.

$$factor(45s^{2}-120s+80)$$

Koeffitsientlarning eng katta umumiy omillarini topish.

$$gcf(45,-120,80)=5$$

5 omili.

$$5\left(9s^{2}-24s+16\right)$$

Asosiy a'zoning kvadrat ildizini topish, 9s^{2}.

$$\sqrt{9s^{2}}=3s$$

Ergashuvchi shartning kvadrat ildizini topish, 16.

$$\sqrt{16}=4$$

Trinomal kvadrat bu binomialning kvadrati bo'lib, tinomial kvadratning o'rta shart belgisi bilan ifodalangan belgiga ega old va ergashuvchi shartlarning kvadratidagi ildiz yig'indisi yoki farqidir.

$$5\left(3s-4\right)^{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.

$$45s^{2}-120s+80=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$s=\frac{-\left(-120\right)±\sqrt{\left(-120\right)^{2}-4\times 45\times 80}}{2\times 45}$$

-120 kvadratini chiqarish.

$$s=\frac{-\left(-120\right)±\sqrt{14400-4\times 45\times 80}}{2\times 45}$$

-4 ni 45 marotabaga ko'paytirish.

$$s=\frac{-\left(-120\right)±\sqrt{14400-180\times 80}}{2\times 45}$$

-180 ni 80 marotabaga ko'paytirish.

$$s=\frac{-\left(-120\right)±\sqrt{14400-14400}}{2\times 45}$$

14400 ni -14400 ga qo'shish.

$$s=\frac{-\left(-120\right)±\sqrt{0}}{2\times 45}$$

0 ning kvadrat ildizini chiqarish.

$$s=\frac{-\left(-120\right)±0}{2\times 45}$$

-120 ning teskarisi 120 ga teng.

$$s=\frac{120±0}{2\times 45}$$

2 ni 45 marotabaga ko'paytirish.

$$s=\frac{120±0}{90}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{4}{3} ga va x_{2} uchun \frac{4}{3} ga bo‘ling.

$$45s^{2}-120s+80=45\left(s-\frac{4}{3}\right)\left(s-\frac{4}{3}\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{4}{3} ni s dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$45s^{2}-120s+80=45\times \frac{3s-4}{3}\left(s-\frac{4}{3}\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{4}{3} ni s dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$45s^{2}-120s+80=45\times \frac{3s-4}{3}\times \frac{3s-4}{3}$$

Raqamlash sonlarini va maxraj sonlariga ko'paytirish orqali \frac{3s-4}{3} ni \frac{3s-4}{3} ga ko'paytirish. So'ngra kasrni imkoni boricha eng kam a'zoga qisqartiring.

$$45s^{2}-120s+80=45\times \frac{\left(3s-4\right)\left(3s-4\right)}{3\times 3}$$

3 ni 3 marotabaga ko'paytirish.

$$45s^{2}-120s+80=45\times \frac{\left(3s-4\right)\left(3s-4\right)}{9}$$

45 va 9 ichida eng katta umumiy 9 faktorini bekor qiling.

$$45s^{2}-120s+80=5\left(3s-4\right)\left(3s-4\right)$$

Baholash

$$5\left(3s-4\right)^{2}$$