Exploring Algebraic Identities Mind Map

An algebraic identity is true for all allowed values of the variable, while an equation is true only for particular values that satisfy it.

If both sides remain equal after substituting different values, it is likely an identity; if only selected values work, it is an equation.

Square identities are standard expansions for (a+b)^2, (a-b)^2, and (a+b)(a-b) used to simplify products quickly.

For a square of a binomial, always write three terms; for sum multiplied by difference, write two terms.

Cube identities are standard formulas for expanding or factorising expressions involving cubes of binomials and sums or differences of cubes.

In sum of cubes, the bracket sign is plus and the middle sign in the trinomial is minus; in difference of cubes, these signs reverse.

Factorisation using identities means rewriting an expression as a product by matching it with a known algebraic identity.

Before factorising a three-term expression as a perfect square, check whether the middle term is exactly twice the product of the square roots.

Algebra-tiles visualisation uses squares and rectangles to represent algebraic areas and understand identities geometrically.

In a diagram for (a+b)^2, look for two identical rectangles of area ab.

Three-variable identities expand or factorise expressions containing a, b, and c together, especially (a+b+c)^2 and a^3+b^3+c^3-3abc.

For (a+b+c)^2, write all three squares first, then all three pair products doubled.

Simplifying rational expressions means factorising numerator and denominator, cancelling common non-zero factors, and stating restrictions where needed.

Factor first, cancel only full common factors, and mention the denominator restriction if the expression has variables.