AC9M9A02Year 9AlgebraPractised on site

AC9M9A02 — Year 9 Algebra

Official Curriculum Content Description:

simplify algebraic expressions, expand binomial products and factorise monic quadratic expressions

Worked Examples (3)

Example 1Factorising Monic Quadratics

Factorise

x^2 + 2x + 1

Common mistake: Sign error in the constant terms

Correct Answer:

(x + 1)(x + 1)

Worked Solution:

Find two numbers that multiply to give 1 and add to give 2: The numbers are 1 and 1.

(1) \times (1) = 1

and

(1) + (1) = 2

= (x + 1)(x + 1)

Example 2Expanding Double Brackets

Expand and simplify

(x - 6)(x - 6)

Common mistake: Multiplying only first and last terms (forgetting middle terms)

Correct Answer:

x^2 - 12x + 36

Worked Solution:

Multiply every term in the first bracket by every term in the second bracket:

(x)(x) + (x)((-6)) + (-6)(x) + (-6)((-6))

= x^2 - 12x + 36

= x^2 - 12x + 36

Example 3Difference of Two Squares Factorisation

Factorise

x^2 - 1

Common mistake: Confusing difference of two squares with a perfect square (e.g. (x - k)²)

Correct Answer:

(x + 1)(x - 1)

Worked Solution:

Use the difference of two squares identity,

p^2 - q^2 = (p + q)(p - q)

: Here,

p = x

and

q = 1

= (x + 1)(x - 1)

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