Factorising using the difference of two squares | Maths

Starter quiz

Expand and simplify the expression: $(3x + 2)(x - 4)(4x + 1)$

$12x^3 - 37x^2 + 42x - 8$

$12x^3 + 37x^2 - 42x + 8$

$12x^3 - 37x^2 - 42x - 8$ ✓
Expand and simplify the expression: $(2x + 1)(3x - 2)(x - 4)$

$6x^3 - 25x^2 + 2x + 8$ ✓

$6x^3 + 25x^2 - 2x - 8$

$6x^3 - 25x^2 - 2x + 8$
Factorise $x^2 + 5x + 6$

'(x + 2)(x + 3)' ✓
Factorise $x^2 + 7x + 10$

'(x + 5)(x + 2)' ✓
Factorise $x^2 + 3x - 4$

'(x - 1)(x + 4)' ✓
Factorise $x^2 - x - 6$

'(x - 3)(x + 2)' ✓

Exit quiz

Factorise this expression $x^2 - 25$

'(x - 5)(x + 5)' ✓
Factorise this expression $y^2 - 49$

'(y - 7)(y + 7)' ✓
Factorise this expression $4x^2 - 9$

'(2x - 3)(2x + 3)' ✓
Factorise this expression $9y^2 - 16$

'(3y - 4)(3y + 4)' ✓
Factorise this expression $16x^2 - 81$

'(4x - 9)(4x + 9)' ✓
Factorise this expression $25y^2 - 64$

'(5y - 8)(5y + 8)' ✓

Worksheet

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Lesson Details

Key learning points

When the coefficient of the x term is zero, you may still be able to factorise.
There is a structure to the quadratic expressions that can be factorised if there is no x term.
The same area model can be used to explore this structure.

Common misconception

Once shown the difference of two squares, pupils may think that squaring each term in a binomial is the correct way to expand binomials such as (x+3)^2

Spend time investigating where the difference of two squares occurs, use representations such as algebra tiles and area models.

Keywords

Factorise - To factorise is to express a term as the product of its factors.
Quadratic - A quadratic is an equation, graph, or sequence whereby the highest exponent of the variable is 2
Absolute value - The absolute value of a number is its distance from zero.