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. \( \begin{array}{ll}\text { A) }\left(x^{2}+1\right)^{3} & \text { B) }\left(y^{2}+1\right)^{3}\end{array} \)

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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.

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To'g'ri javob B) \( (y^{2} + 1)^{3} \).
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