সপ্তম শ্রেণীর বীজগণিত ৫.২ অধ্যায়ের সূত্রের সাহায্যে গুণফল নির্ণয়ের কয়েকটি কঠিন প্রশ্ন উত্তরসহ দেওয়া হলো।
৬/ গুণফল নির্ণয়:
(a - b - c) (a + b + c)
= {a - (b + c)} {a + (b + c)}
= a2 - (b + c)2
= a2 - (b2 + 2bc + c2)
= a2 - b2 - 2bc - c2
= a2 - b2 - c2 - 2bc (Ans)
= {a - (b + c)} {a + (b + c)}
= a2 - (b + c)2
= a2 - (b2 + 2bc + c2)
= a2 - b2 - 2bc - c2
= a2 - b2 - c2 - 2bc (Ans)
৭/ গুণফল নির্ণয়:
(x2 - x + 1) (x2 + x + 1)
= {(x2 + 1) - x} {(x2 + 1) + x}
= (x2 + 1)2 - x2
= (x2)2 + 2 . x2 . 1 + 12 - x2
= x4 + 2x2 + 1 - x2
= x4 + x2 + 1 (Ans)
= {(x2 + 1) - x} {(x2 + 1) + x}
= (x2 + 1)2 - x2
= (x2)2 + 2 . x2 . 1 + 12 - x2
= x4 + 2x2 + 1 - x2
= x4 + x2 + 1 (Ans)
৮) (x - 1⁄2a)(x - 5⁄2a)
= x2 + { -1⁄2a + (-5⁄2a) }x + (-1⁄2a)(-5⁄2a)
= x2 + (-a⁄2 - 5a⁄2)x + a⁄2 ⋅ 5a⁄2
= x2 + (-a - 5a⁄2)x + 5a2⁄4
= x2 + (-6a⁄2)x + 5a2⁄4
= x2 - 3ax + 5a2⁄4
সূত্র: (x + a)(x + b) = x2 + (a + b)x + ab
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