(a + b)^{2} = a^{2} + 2ab + b^{2}

(a – b)^{2} = a^{2} – 2ab + b^{2}

(a + b)(a – b) = a^{2} – b^{2}

(x + a)(x + b) = x^{2} + (a + b)x + ab

(ax + b)(cx + d) = acx^{2} + (ad + bc)x + bd

(a + b)^{3} = a^{3} + 3ab(a + b) + b^{3}

(a – b)^{3} = a^{3} – 3ab(a – b) – b^{3}

(a + b)(a^{2} – ab + b^{2}) = a^{3} + b^{3}

(a – b)(a^{2} + ab + b^{2}) = a^{3} – b^{3}

**Deductions**

(a + b)^{2} + (a – b)^{2} = 2(a^{2} + b^{2})

(a + b)^{2} – (a – b)^{2} = 4ab

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