Grade 10 Maths Essentials: Algebraic Expressions and Factorisation

Practice flashcards covering terminology and methods for Grade 10 algebraic expressions and factorisation.

Numerical Coefficient

The number in front of a variable.

Variable

An algebraic letter(s) used to represent unknown(s).

Constant

The numerical term in an algebraic expression.

Algebraic Expression

A mathematical expression made up of one or more terms separated by addition ($+$) or subtraction ($-$).

Polynomial

An algebraic expression where the exponent(s) on the variable(s) are natural numbers.

Monomial

An algebraic expression consisting of one term, such as $4$ or $2a^{2}be$.

Binomial

An algebraic expression consisting of two terms, such as $6x + 2y$.

Trinomial

An algebraic expression consisting of three terms, such as $6x^{2} - 5x + 4$.

Degree

The highest value of an exponent of a specific variable in an algebraic expression (e.g., $7x^{3} - 3xy + 8x^{6} + 4$ has the sixth degree in $x$ and first degree in $y$).

Like Terms

Terms with the same variable(s) and the same exponents, though the numerical coefficients may differ.

Unlike Terms

Terms where the variables are different, such as $2x$, $2x^{2}$, and $3xy$.

BODMAS rule

The rule followed to simplify expressions; addition and subtraction are only performed on like terms, and answers are written in alphabetical order with descending powers.

Distributive Law

The method used to multiply a monomial by a polynomial, such as $2a^{2}(3a^{2} + 4ab - a^{3}c)$.

FOIL method

An acronym for Firsts, Outers, Inners, Lasts; used for multiplying a binomial by a binomial.

Squaring a Binomial

A three-step process: 1) Square the first term, 2) Multiply the first and second terms and double the result, 3) Square the last term.

Difference of Two Squares (Products)

A product involving two binomials that are identical except for the middle sign, resulting in the first term squared minus the last term squared (e.g., $(3a - 2b)(3a + 2b) = 9a^{2} - 4b^{2}$).

Binomial by a Trinomial

Multiplication where each term in the binomial is multiplied by each term in the trinomial, often resulting in a sum or difference of two cubes.

Factorisation

The inverse operation to products, which involves putting brackets back into a mathematical sum.

Highest Common Factor (HCF)

The first step in factorisation and the inverse of distribution, involving identifying the greatest common element among terms.

Sign change

A technique used to make factors identical by changing the sign in a bracket, specifically transforming $(b - a)$ into $-1(a - b)$.

Difference of Two Squares (DOTS) (Factorisation)

A factorisation method involving taking the square root of the first term minus the square root of the second term in one bracket, and the square root of the first term plus the square root of the second term in the other.

Grouping

A factorisation method used for expressions with four or more terms by identifying patterns such as HCF, DOTS, or perfect square trinomials.

Trinomial Standard Form

The form $ax^{2} + bx + c$ used for factorising trinomial expressions.

Perfect Square Trinomial

A trinomial where the first and last terms are perfect squares, such as $4m^{2} - 12mn + 9n^{2} = (2m - 3n)^{2}$.