Mathematics·Algebra · NSSCO 6.1
Algebraic expressions: expand & factorise
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Algebra is just arithmetic with letters standing in for numbers, and this lesson makes it feel friendly. We learn the language of terms and like terms, tidy expressions by collecting like terms, then multiply out single and double brackets — including the two special products you must know by heart. After that we go backwards: factorising by common factor, factorising quadratics and the difference of two squares. We finish with simplifying and combining algebraic fractions, and substituting numbers back in. Every rule is said out loud and every line is drawn as we go.
What you'll learn in this lesson
By the end you should be able to (NSSCO Mathematics 6.1):
- Use letters to stand for numbers, and name the parts of an expression (term, coefficient, like terms)
- Simplify expressions by collecting like terms, and by multiplying and dividing terms using the laws of indices
- Multiply a monomial by a polynomial — expand single brackets
- Expand the product of two brackets, including perfect squares (x+a)² and the difference of two squares (x+a)(x−a)
- Factorise by extracting common factors, and factorise by grouping
- Factorise quadratics of the form x²+bx+c and simple ax²+bx+c
- Factorise the difference of two squares
- Simplify algebraic fractions by factorising, and add and subtract them using a common denominator
- Substitute numbers into algebraic expressions and evaluate them
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