1.5-bo'lim : Ko'p nomlilarni ko'paytuvchilarga ajratish
5. Quyidagi ko‘phadni guruhlash orqali ko‘paytiring.
\[7x + 7{x^3} + {x^4} + {x^6}\]Yechim
Bu erda birinchi qadam birinchi ikkita atama va oxirgi ikki atamani quyidagicha guruhlashdir.
\[\left( {7x + 7{x^3}} \right) + \left( {{x^4} + {x^6}} \right)\]2-qadam
Endi biz birinchi guruhdan 7\(x\) ni va ikkinchi guruhdan \({x^4}\) ni faktor qilishimiz mumkinligini ko'ramiz. Shunday qilib,
\[7x + 7{x^3} + {x^4} + {x^6} = 7x\left( {1 + {x^2}} \right) + {x^4}\left( {1 + {x^2}} \right)\]3-qadam
Va nihoyat, biz ikkala yangi shartdan \(x\left( {1 + {x^2}} \right)\) ni olishimiz mumkinligini ko'ramiz,
\[7x + 7{x^3} + {x^4} + {x^6} = \require{bbox} \bbox[2pt,border:1px solid black]{{x\left( {1 + {x^2}} \right)\left( {7 + {x^3}} \right)}}\]