Algebraic Formulas (Special Products)

(a + b)2 = a2 + 2ab + b2

(a – b)2 = a2 – 2ab + b2

(a + b)(a – b) = a2 – b2

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

(ax + b)(cx + d) = acx2 + (ad + bc)x + bd

(a + b)3 = a3 + 3ab(a + b) + b3

(a – b)3 = a3 – 3ab(a – b) – b3

(a + b)(a2 – ab + b2) = a3 + b3

(a – b)(a2 + ab + b2) = a3 – b3

Deductions

(a + b)2 + (a – b)2 = 2(a2 + b2)

(a + b)2 – (a – b)2 = 4ab

Numerical calculations can be performed more conveniently with the help of special products, often called algebraic formulae.