# Algebraic identities

### Binomial Algebraic identities

List of algebraic formulas to Expand square of sum and subtraction of two terms.

$(1) \,\,\,\,\,\,$ ${(a+b)}^2 \,=\, a^2+b^2+2ab$

$(2) \,\,\,\,\,\,$ ${(a-b)}^2 \,=\, a^2+b^2-2ab$

An algebraic formula to Expand product of sum and subtraction of two terms.

$(a+b)(a-b) \,=\, a^2-b^2$

List of algebraic formulas to Expand cube of sum and subtraction of two terms.

$(1) \,\,\,\,\,\,$ ${(a+b)}^3 \,=\, a^3+b^3+3ab(a+b)$

$(2) \,\,\,\,\,\,$ ${(a-b)}^3 \,=\, a^3-b^3-3ab(a-b)$

### Trinomial Algebraic identities

List of algebraic formulas to Expand square of sum and subtraction of three terms.

$(1) \,\,\,\,\,\,$ ${(a+b+c)}^2$ $=$ $a^2+b^2+c^2$ $+$ $2ab+2bc+2ca$

$(2) \,\,\,\,\,\,$ ${(a+b-c)}^2$ $=$ $a^2+b^2+c^2$ $+$ $2ab-2bc-2ca$

$(3) \,\,\,\,\,\,$ ${(a-b+c)}^2$ $=$ $a^2+b^2+c^2$ $-2ab-2bc+2ca$

$(4) \,\,\,\,\,\,$ ${(a-b-c)}^2$ $=$ $a^2+b^2+c^2$ $-2ab+2bc-2ca$

### Special Product of Binomials

$(1) \,\,\,\,\,\,$ ${(x+a)}{(x+b)}$ $\,=\,$ $x^2+{(a+b)}x+ab$

$(2) \,\,\,\,\,\,$ ${(x+a)}{(x-b)}$ $\,=\,$ $x^2+{(a-b)}x-ab$

$(3) \,\,\,\,\,\,$ ${(x-a)}{(x+b)}$ $\,=\,$ $x^2-{(a-b)}x-ab$

$(4) \,\,\,\,\,\,$ ${(x-a)}{(x-b)}$ $\,=\,$ $x^2-{(a+b)}x+ab$