Algebraic sources up to 6-10:
☞ (a+b)²=a²+2ab+b²
☞ (a+b)²=(a-b)²+4ab
☞ (a-b)²=a²-2ab+b²
☞ (a-b)²=(a+b)²-4ab
☞ a²+b²=(a+b)²-2ab
☞ 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=(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
