• a² + b²= (a-b)²+2ab

• a²-b²= (a +b)(a -b)

• 2(a²+b²)= (a+b)²+(a-b)²

• 4ab = (a+b)²-(a-b)²

• ab = {(a+b)/2}²-{(a-b)/2}²

• (a+b+c)² = a²+b²+c²+2(ab+bc+ca)

• (a+b)³ = a³+3a²b+3ab²+b³

• (a+b)³ = a³+b³+3ab(a+b)

• a-b)³= a³-3a²b+3ab²-b³

• (a-b)³= a³-b³-3ab(a-b)

• a³+b³= (a+b) (a²-ab+b²)

• a³+b³= (a+b)³-3ab(a+b)

•  a³-b³ = (a-b) (a²+ab+b²)

• a³-b³ = (a-b)³+3ab(a-b)

• (a² + b² + c²) = (a + b + c)² – 2(ab + bc + ca)

• 2 (ab + bc + ca) = (a + b + c)² – (a² + b² + c²)

• (a + b + c)³ = a³ + b³ + c³ + 3 (a + b) (b + c) (c + a)

• a³ + b³ + c³ – 3abc =(a+b+c)(a² + b²+ c²–ab–bc– ca)

• a3 + b3 + c3 – 3abc =½ (a+b+c) { (a–b)²+(b–c)²+(c–a)²}

• (x + a) (x + b) = x² + (a + b) x + ab

• (x + a) (x – b) = x² + (a – b) x – ab

• (x – a) (x + b) = x² + (b – a) x – ab

• (x – a) (x – b) = x² – (a + b) x + ab

• (x+p) (x+q) (x+r) = x³ + (p+q+r) x² + (pq+qr+rp) x +pqr

• bc (b-c) + ca (c- a) + ab (a – b) = – (b – c) (c- a) (a – b)

• a² (b- c) + b² (c- a) + c² (a – b) = -(b-c) (c-a) (a – b)

• a (b² – c²) + b (c² – a²) + c (a² – b²) = (b – c) (c- a) (a – b)

• a³ (b – c) + b³ (c-a) +c³ (a -b) =- (b-c) (c-a) (a – b)(a + b + c)

• b²-c² (b²-c²) + c²a²(c²-a²)+a²b²(a²-b²)=-(b-c) (c-a) (a-b) (b+c) (c+a) (a+b)

• (ab + bc+ca) (a+b+c) – abc = (a + b)(b + c) (c+a)

• (b + c)(c + a)(a + b) + abc = (a + b +c) (ab + bc + ca)