Factorisation and Binomial Expansion Lecture Notes

This set of vocabulary flashcards covers fundamental concepts of algebraic factorisation, the distributive law, binomial expansion, and the factorisation of quadratic expressions based on the provided lecture materials.

Factorisation

The process of rewriting an algebraic expression as a product of its factors, which is the reverse of expanding.

Expanding

The process of removing brackets from an algebraic expression by multiplying terms.

Factorised form

An expression written as a product of factors, such as $3(x+2)$.

Expanded form

The resulting expression after brackets have been removed, such as $3x+6$.

Highest Common Factor (HCF)

The largest factor that is shared by two or more terms; for example, the HCF of $5x^2$ and $10x$ is $5x$, and the HCF of $15ab^2$ and $15a^2b$ is $15ab$.

Distributive Law

A rule used to expand and remove brackets by multiplying a term outside the brackets by each term inside, expressed as $a(b+c) = ab + ac$.

Distributive Law with Negative terms

The application of the distributive law involving negative signs, such as $-a(b+c) = -ab - ac$ or $-a(b-c) = -ab + ac$.

Factoring out the negative sign

A factorisation method where a negative sign is included as part of the HCF, as seen in $-8x-4 = -4(2x+1)$.

Binomial Product Expansion

The process of expanding the product of two binomials using the rule $(a+b)(c+d) = a(c+d) + b(c+d) = ac + ad + bc + bd$. For example, $(x+1)(x+5) = x^2 + 5x + x + 5 = x^2 + 6x + 5$.

Quadratic Expression Factorisation

The process of rewriting a trinomial of the form $x^2+bx+c$ into two binomial factors, such as $x^2+8x+12 = (x+6)(x+2)$, by finding numbers that multiply to $c$ and add to $b$.