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Year 10
Higher

Checking and securing understanding of the product of two binomials

I can use the distributive law to find the product of two binomials.

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New
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Year 10
Higher

Checking and securing understanding of the product of two binomials

I can use the distributive law to find the product of two binomials.

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Share activities with pupils
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Lesson details

Key learning points

  1. The distributive law can be used to find the product of two binomials.
  2. An area model can be used to explore the underlying structure.
  3. Both of the terms in one bracket must be multiplied by both terms in the second.

Keywords

  • Binomial - A binomial is an algebraic expression representing the sum or difference of exactly 2 unlike terms.

  • Partial product - Any of the multiplication results that lead up to an overall multiplication result.

Common misconception

Missing out partial products.

Use an area model to demonstrate this. If pupils do not wish to draw the models they should be using the distributive law instead e.g. (x + 2)(x + 3) as x(x + 3)+2(x + 3)

Modelling the product of two binomials with algebra tiles, area models and distributive law are all used when factorising quadratics. Make sure pupils are confident with these representations so they can begin to work backwards using the patterns and structures they spot.
Teacher tip

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.
What is the value of $$x$$ for $$3x + 5 = 2(x - 2)$$?
Correct Answer: -9
Q2.
What is the value of $$x$$ for $$\frac{5x + 15}{3} = \frac{2x - 2}{2}$$?
Correct Answer: -9
Q3.
What is the positive value of $$x$$ for $$x^2 - 4x - 12 = 0$$?
Correct Answer: 6
Q4.
Rearrange for $$x$$: $$3y - x = 15$$?
$$x = 3y + 15$$
$$x = 15 - 3y$$
Correct answer: $$x = 3y - 15$$
Q5.
Make $$b$$ the subject for $$a + 2b = 10$$
Correct answer: $$b = \frac{10-a}{2}$$
$$b = \frac{a-10}{2}$$
$$b = \frac{a}{20}$$
Q6.
Make $$p$$ the subject of $$\frac{2p + q}{3} = 4$$
$$p = 4 - \frac{q}{3}$$
Correct answer: $$p = 6 - \frac{q}{2}$$
$$p = 2q + 12$$

Exit quiz

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6 Questions

Q1.
Expand and simplify the expression: $$(x + 3)(x - 2)$$
$$x^2 - x + 6$$
Correct answer: $$x^2 + x - 6$$
$$x^2 + 5x - 6$$
Q2.
Expand and simplify the expression: $$2(x - 1)(x + 5)$$
$$2x^2 + 10x - 2$$
$$2x^2 - 10x + 10$$
Correct answer: $$2x^2 + 8x - 10$$
Q3.
Expand and simplify the expression: $$3(x + 2)^2$$
Correct answer: $$3x^2 + 12x + 12$$
$$3x^2 + 6x + 6$$
$$3x^2 + 12x + 36$$
Q4.
Expand and simplify the expression: $$(2x - 3)(x + 4)$$
$$2x^2 + 8x - 12$$
$$2x^2 - x - 12$$
Correct answer: $$2x^2 + 5x - 12$$
Q5.
Expand and simplify the expression: $$-x(2x - 5)(3x + 1)$$
$$-6x^3 - x^2 + 5x$$
Correct answer: $$-6x^3 + 13x^2 + 5x$$
$$-6x^3 + x^2 - 5x$$
Q6.
Expand and simplify the expression: $$4(y + 3)(2y - 3)$$
$$8y^2 - 36$$
Correct answer: $$8y^2 + 12y - 36$$
$$8y^2 - 12y - 36$$