GCSE Maths - Algebra
Algebra does NOT have to be scary. Once you understand, it’s actually super easy
Algebra does not have to be difficult. Once the key methods are understood, questions become
much more manageable. This revision sheet covers the essential algebra skills for both Foundation
and Higher tiers, with clear explanations and examples based on the 2026 GCSE specification.
Collecting like terms Powers and Roots
> Like terms have the same variable and power > x² means x × x
> Add or subtract coefficients only √
> x is the number that squares to give x
> Example: 3x + 5x 2x = 6x − √
> Examples: 16 = 4 or 5² = 25
Rules of Indices (Negative Powers) Rules of Indices (Fractional Powers- Higher)
>x⁻¹ = 1/x √
> x¹ᐟ² = x
>Rules: > x¹ᐟ³ = ∛x
xᵃ × xᵇ = xᵃ⁺ᵇ > Examples:
xᵃ ÷ xᵇ = xᵃ⁻ᵇ >>16¹ᐟ² = 4
> Example: x⁻² = 1/x² >>27¹ᐟ³ = 3
Expanding single brackets Expanding double brackets
> Multiply the term outside the bracket by > Multiply every term in the first bracket by
each term inside. every term in the second.
> Examples: > Example:
>> 4(x + 3) = 4x + 12 >> (x + 2)(x + 5) = x² + 7x + 10
>> 3(2x 5) = 6x + 15 − − −
Expanding triple brackets (Higher) Factorising into single brackets
> Expand two brackets first, then multiply by > Take out the highest common factor (HCF).
the third. > Example: 6x + 12 = 6(x + 2)
> Example:
>> (x + 1)(x + 2)(x + 3) = (x² + 3x + 2)(x + 3) Surds - Rationalising (Higher)
> Remove surds from the denominator.
Surds - The Basics (Higher) > Example:
> A surd contains a square root that cannot be
simplified.
√ √ √ √
>> 1/ 5 × 5/ 5 = 5/5
> Example:
>> 8 = (4 × 2) = 2 2 √ √ √
@atg.w
Algebra does NOT have to be scary. Once you understand, it’s actually super easy
Algebra does not have to be difficult. Once the key methods are understood, questions become
much more manageable. This revision sheet covers the essential algebra skills for both Foundation
and Higher tiers, with clear explanations and examples based on the 2026 GCSE specification.
Collecting like terms Powers and Roots
> Like terms have the same variable and power > x² means x × x
> Add or subtract coefficients only √
> x is the number that squares to give x
> Example: 3x + 5x 2x = 6x − √
> Examples: 16 = 4 or 5² = 25
Rules of Indices (Negative Powers) Rules of Indices (Fractional Powers- Higher)
>x⁻¹ = 1/x √
> x¹ᐟ² = x
>Rules: > x¹ᐟ³ = ∛x
xᵃ × xᵇ = xᵃ⁺ᵇ > Examples:
xᵃ ÷ xᵇ = xᵃ⁻ᵇ >>16¹ᐟ² = 4
> Example: x⁻² = 1/x² >>27¹ᐟ³ = 3
Expanding single brackets Expanding double brackets
> Multiply the term outside the bracket by > Multiply every term in the first bracket by
each term inside. every term in the second.
> Examples: > Example:
>> 4(x + 3) = 4x + 12 >> (x + 2)(x + 5) = x² + 7x + 10
>> 3(2x 5) = 6x + 15 − − −
Expanding triple brackets (Higher) Factorising into single brackets
> Expand two brackets first, then multiply by > Take out the highest common factor (HCF).
the third. > Example: 6x + 12 = 6(x + 2)
> Example:
>> (x + 1)(x + 2)(x + 3) = (x² + 3x + 2)(x + 3) Surds - Rationalising (Higher)
> Remove surds from the denominator.
Surds - The Basics (Higher) > Example:
> A surd contains a square root that cannot be
simplified.
√ √ √ √
>> 1/ 5 × 5/ 5 = 5/5
> Example:
>> 8 = (4 × 2) = 2 2 √ √ √
@atg.w
