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Year 10
Higher

Factorising using the difference of two squares

I can factorise quadratics of the form x^2 + bx + c including using the difference of two squares.

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New
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Year 10
Higher

Factorising using the difference of two squares

I can factorise quadratics of the form x^2 + bx + c including using the difference of two squares.

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Lesson details

Key learning points

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

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.

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.

Showing the use of the distributive law alongside an area model can help pupils factorise more complex quadratics in the future. Pupils who wish to move away from the models can then use this method to expand and factorise.
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Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Expand and simplify the expression: $$(3x + 2)(x - 4)(4x + 1)$$
$$12x^3 - 37x^2 + 42x - 8$$
$$12x^3 + 37x^2 - 42x + 8$$
Correct answer: $$12x^3 - 37x^2 - 42x - 8$$
Q2.
Expand and simplify the expression: $$(2x + 1)(3x - 2)(x - 4)$$
Correct answer: $$6x^3 - 25x^2 + 2x + 8$$
$$6x^3 + 25x^2 - 2x - 8$$
$$6x^3 - 25x^2 - 2x + 8$$
Q3.
Factorise $$x^2 + 5x + 6$$
Correct Answer: (x + 2)(x + 3), (x + 3)(x + 2)
Q4.
Factorise $$x^2 + 7x + 10$$
Correct Answer: (x + 5)(x + 2), (x + 2)(x + 5)
Q5.
Factorise $$x^2 + 3x - 4$$
Correct Answer: (x - 1)(x + 4), (x + 4)(x - 1)
Q6.
Factorise $$x^2 - x - 6$$
Correct Answer: (x - 3)(x + 2), (x + 2)(x - 3)

Exit quiz

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6 Questions

Q1.
Factorise this expression $$x^2 - 25$$
Correct Answer: (x - 5)(x + 5), (x + 5)(x - 5)
Q2.
Factorise this expression $$y^2 - 49$$
Correct Answer: (y - 7)(y + 7), (y + 7)(y - 7)
Q3.
Factorise this expression $$4x^2 - 9$$
Correct Answer: (2x - 3)(2x + 3), (2x + 3)(2x - 3)
Q4.
Factorise this expression $$9y^2 - 16$$
Correct Answer: (3y - 4)(3y + 4), (3y + 4)(3y - 4)
Q5.
Factorise this expression $$16x^2 - 81$$
Correct Answer: (4x - 9)(4x + 9), (4x + 9)(4x - 9)
Q6.
Factorise this expression $$25y^2 - 64$$
Correct Answer: (5y - 8)(5y + 8), (5y + 8)(5y - 8)