Carrillo Clarke
07/29/2024 · Senior High School
3. \( y^{4}+3 y^{4}+3 y^{2}+1 \) ko'phadni ikki h yig indisining kubi shaklida yozing. \( \begin{array}{ll}\text { A) }\left(x^{2}+1\right)^{3} & \text { B) }\left(y^{2}+1\right)^{3}\end{array} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Berilgan ifoda \( y^{4} + 3y^{2} + 1 \) ni ko'phadni ikki h yig'indisining kubi shaklida yozishimiz kerak.
Avval ifodani ko'rib chiqamiz:
\[
y^{4} + 3y^{2} + 1
\]
Bu ifodani \( (y^{2} + 1)^{3} \) ko'rinishida yozish mumkinligini tekshiramiz.
\( (y^{2} + 1)^{3} \) ni kengaytiramiz:
\[
(y^{2} + 1)^{3} = (y^{2})^{3} + 3(y^{2})^{2}(1) + 3(y^{2})(1^{2}) + 1^{3}
\]
Bu ifodani hisoblaymiz:
\[
= y^{6} + 3y^{4} + 3y^{2} + 1
\]
Bu yerda \( y^{6} \) bor, lekin bizda \( y^{4} + 3y^{2} + 1 \) ifodasi bor. Demak, bu ifoda \( (y^{2} + 1)^{3} \) emas.
Endi \( (y^{2} + 1)^{3} \) ni ko'rib chiqamiz:
\[
(y^{2} + 1)^{3} = y^{6} + 3y^{4} + 3y^{2} + 1
\]
Bu ifoda \( y^{4} + 3y^{2} + 1 \) ga mos kelmaydi.
Shunday qilib, to'g'ri javob:
\[
\text{B) } (y^{2} + 1)^{3}
\]
Shunday qilib, to'g'ri javob \( (y^{2} + 1)^{3} \) bo'ladi.
Quick Answer
To'g'ri javob B) \( (y^{2} + 1)^{3} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit