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Year 10
Higher

The product of three binomials

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

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New
New
Year 10
Higher

The product of three binomials

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

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. The distributive law can be used to find the product of three (or more) binomials.
  2. This can be done by finding the product of two of the binomials first.
  3. The commutative law allows you to choose which two of the binomial expressions to find the product of first.
  4. Sometimes your choice can reduce the complexity.

Common misconception

The first two binomials have to be multiplied first.

Look for features of the binomials that suggest which binomials will be easiest to multiply first. Any order will give the same final product but a particular order may reduce complexity.

Keywords

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

  • Distributive law - The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result.

Encourage clear and full working here. Pupils should be writing mathematically so every line of working is complete. Use of brackets can focus attention on which part of the expression is being manipulated at each step without pupils omitting parts of the expression and forgetting them later.
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).

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Starter quiz

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6 Questions

Q1.
Make $$x$$ the subject of $$4x - 3y = 12$$
$$x = 3y + 12$$
$$x = \frac{12 + 3y}{2}$$
Correct answer: $$x = \frac{12 + 3y}{4}$$
Q2.
Make $$p$$ the subject of $$\frac{p}{2} + q = 7$$
$$p = -2(q - 3.5)$$
$$p = -q - 7$$
Correct answer: $$p = 2(7-q)$$
Q3.
Make $$a$$ the subject of $$3a -\frac{b}{4} + 2 = 0$$
$$a = \frac{b - 4 }{12}$$
$$a = \frac{b - 8 }{4}$$
Correct answer: $$a = \frac{b - 8 }{12}$$
Q4.
Expand and simplify the expression: $$(x + 3)(x - 2)$$
$$x^2 + 2x - 6$$
$$x^2 - x + 6$$
Correct answer: $$x^2 + x - 6$$
Q5.
Expand and simplify the expression: $$2(x + 5)(x - 3)$$
$$2x^2 + 4x - 30$$
Correct answer: $$2x^2 + 2x - 30$$
$$x^2 + 2x - 15$$
Q6.
Expand and simplify the expression: $$x(x+5)(x-2)$$
Correct answer: $$x^3 + 3x^2 - 10x$$
$$x^3 + 5x^2 - 10x$$
$$2x^2+ 3x +10$$

Exit quiz

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6 Questions

Q1.
Expand and simplify the expression: $$(x + 2)(x - 3)(x + 4)$$
$$x^3 - x^2 - 14x + 24$$
$$x^3 + 3x^2 - 2x - 24$$
$$x^3 - 3x^2 + 10x + 24$$
Correct answer: $$x^3 + 3x^2 - 10x - 24$$
Q2.
Expand and simplify the expression: $$(2x - 1)(x + 5)(3x - 2)$$
Correct answer: $$6x^3 + 23x^2 - 33x + 10$$
$$6x^3 + 27x^2 + 7x - 10$$
$$6x^3 - 23x^2 + 33x + 10$$
$$6x^3 - 29x^2 + 13x + 10$$
Q3.
Expand and simplify the expression: $$(y - 2)(2y + 3)(y - 4)$$
$$2y^3 - 3y^2 - 14y + 24$$
Correct answer: $$2y^3 - 9y^2 - 2y + 24$$
$$2y^3 + 5y^2 - 8y - 24$$
$$2y^3 - 5y^2 + 14y - 24$$
Q4.
Expand and simplify the expression: $$(3x + 1)(x - 2)(4x + 5)$$
$$12x^3 + 7x^2 - 33x - 10$$
Correct answer: $$12x^3 - 5x^2 - 33x - 10$$
$$12x^3 - 11x^2 + 3x + 10$$
Q5.
Expand and simplify the expression: $$(2y - 3)(y + 4)(y - 5)$$
$$2y^3 - 3y^2 - 23y + 60$$
$$2y^3 + y^2 - 27y - 60$$
Correct answer: $$2y^3 - 5y^2 - 37y + 60$$
Q6.
Expand and simplify the expression: $$(2x + 1)(3x - 2)(x - 4)$$
$$6x^3 - 17x^2 + 8x + 8$$
$$6x^3 - 25x^2 - 8x + 2$$
Correct answer: $$6x^3 - 25x^2 + 2x + 8$$