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...