1a2b342 5 a62 7 2ab 8 b92 1011

Apuntes

• Subtopic: Binomial Expansion \[ (a+b)^2 = a^2 + 2ab + b^2 \] \[ (a-b)^2 = a^2 - 2ab + b^2 \] \[ (a+b)^2 + (a-b)^2 = 2(a^2 + b^2) \] \[ (a+b)^2 - (a-b)^2 = 4ab \] • Subtopic: Difference of Squares \[ (x+y)(x-y) = x^2 - y^2 \] • Subtopic: Cubic Expansion \[ (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 \] \[ (a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3 \] \[ (a+b)^3 - a^3 + 3ab(a+b) + b^3 \] \[ (a-b)^3 = a^3 - 3ab(a-b) - b^3 \] • Subtopic: Sum and Difference of Cubes \[ a^3 - b^3 = (a-b)(a^2 + ab + b^2) \] \[ a^3 + b^3 = (a+b)(a^2 - ab + b^2) \]