Difference of two squares
I can use the special case when the product of two binomials is the difference of two squares.
Difference of two squares
I can use the special case when the product of two binomials is the difference of two squares.
Lesson details
Key learning points
- The product of two binomials often produces three terms.
- There are cases where the coefficient of the linear term is zero.
- The terms in the two binomials can indicate this.
- You can use an area model to explore the structure.
Common misconception
Squaring a binomial is the same as just squaring each term. This can then cause confusion with difference of two squares where expanding a pair of binomials does result in just two terms.
Using an area model and taking time to check the partial products each time, particularly with negative terms, should help students to check if they have expanded correctly.
Keywords
Partial product - A partial product refers to any of the multiplication results that lead up to an overall multiplication result.
Binomial - A binomial is an algebraic expression representing the sum or difference of exactly two unlike terms.
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).
Video
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Starter quiz
6 Questions
$$(x+3)(x+2)$$ -
$$x^2 + 5x + 6$$
$$(x+3)(x-2)$$ -
$$x^2 + x - 6$$
$$(x+2)(x-3)$$ -
$$x^2 - x - 6$$
$$(x-2)(x-3)$$ -
$$x^2 - 5x + 6$$
$$(x - 6)(x + 1)$$ -
$$x^2 - 5x - 6$$
$$(x + 6)(x -1)$$ -
$$x^2 + 5x - 6$$
Exit quiz
6 Questions
$$(x + 8)(x + 8)$$ -
$$x^2 + 16x + 64$$
$$(x + 8)(x - 8)$$ -
$$x^2 - 64$$
$$(x - 8)(x - 8)$$ -
$$x^2 - 16x + 64$$
$$(x + 2)(x - 2)$$ -
$$x^2 - 4$$
$$(2 + x)(2 - x)$$ -
$$4 - x^2$$
$$(x + 4)(x - 4)$$ -
$$x^2 - 16$$
$$(4 - x)(4 + x)$$ -
$$16 - x^2$$
$$(x - 8)(x + 8)$$ -
$$x^2 - 64$$
$$(8 - x)(8 + x)$$ -
$$64 - x^2$$