বীজগাণিতিক সূত্রাবলী
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(a+b)²= a²+2ab+b²
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(a+b)²= (a-b)²+4ab
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(a-b)²= a²-2ab+b²
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(a-b)²= (a+b)²-4ab
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a² + b²= (a+b)²-2ab
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a² + b²= (a-b)²+2ab
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a²-b²= (a +b)(a -b)
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2(a²+b²)= (a+b)²+(a-b)²
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4ab = (a+b)²-(a-b)²
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ab = {(a+b)/2}²-{(a-b)/2}²
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(a+b+c)² = a²+b²+c²+2(ab+bc+ca)
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(a+b)³ = a³+3a²b+3ab²+b³
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(a+b)³ = a³+b³+3ab(a+b)
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a-b)³= a³-3a²b+3ab²-b³
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(a-b)³= a³-b³-3ab(a-b)
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a³+b³= (a+b) (a²-ab+b²)
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a³+b³= (a+b)³-3ab(a+b)
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a³-b³ = (a-b) (a²+ab+b²)
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a³-b³ = (a-b)³+3ab(a-b)
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(a² + b² + c²) = (a + b + c)² – 2(ab + bc + ca)
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2 (ab + bc + ca) = (a + b + c)² – (a² + b² + c²)
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(a + b + c)³ = a³ + b³ + c³ + 3 (a + b) (b + c) (c + a)
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a³ + b³ + c³ – 3abc =(a+b+c)(a² + b²+ c²–ab–bc– ca)
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a3 + b3 + c3 – 3abc =½ (a+b+c) { (a–b)²+(b–c)²+(c–a)²}
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(x + a) (x + b) = x² + (a + b) x + ab
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(x + a) (x – b) = x² + (a – b) x – ab
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(x – a) (x + b) = x² + (b – a) x – ab
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(x – a) (x – b) = x² – (a + b) x + ab
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(x+p) (x+q) (x+r) = x³ + (p+q+r) x² + (pq+qr+rp) x +pqr
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bc (b-c) + ca (c- a) + ab (a – b) = – (b – c) (c- a) (a – b)
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a² (b- c) + b² (c- a) + c² (a – b) = -(b-c) (c-a) (a – b)
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a (b² – c²) + b (c² – a²) + c (a² – b²) = (b – c) (c- a) (a – b)
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a³ (b – c) + b³ (c-a) +c³ (a -b) =- (b-c) (c-a) (a – b)(a + b + c)
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b²-c² (b²-c²) + c²a²(c²-a²)+a²b²(a²-b²)=-(b-c) (c-a) (a-b) (b+c) (c+a) (a+b)
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(ab + bc+ca) (a+b+c) – abc = (a + b)(b + c) (c+a)
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(b + c)(c + a)(a + b) + abc = (a + b +c) (ab + bc + ca)
