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The product of two binomials

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

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Lesson 3 of 12

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Year 9

The product of two binomials

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

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Lesson details

Key learning points

The distributive law can be used to find the product of two binomials.
An area model can be used to explore the underlying structure.
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 two unlike terms

Common misconception

Missing out partial products

Relating back to numerical examples and showing that 12 × 34 is not just 10 × 30 + 2 × 4. Using algebra tiles and area models can help to support student's understanding.

It will be really valuable for pupils to see the connection between using an area model to multiply two two-digit numbers and multiplying a binomial. Show the two side by side as much as possible.

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This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Worksheet

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Prior knowledge starter quiz

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6 Questions

Q1.
$$2x$$ and $$5x$$ can be called __________ terms.

equivalent

identical

inverse

Correct answer: like

reciprocal

Q2.
What expression could these algebra tiles represent?

Correct answer: $$x^2 + 6x + 9 $$

$$6x^2 + 9 $$

$$7x + 9$$

$$4x^2 + 9x$$

$$x^2 + 15x$$

Q3.
Which is the correct area model to show the expansion of $$x(x + 3)$$?

Correct Answer: An image in a quiz

Q4.
Expand $$x(x + 8)$$.

$$2x + 8$$

$$10x$$

$$9x^2$$

$$x^2 + 8$$

Correct answer: $$x^2 + 8x$$

Q5.
Expand $$x(x - 3)$$.

$$x^2 + 3x$$

Correct answer: $$x^2 - 3x$$

$$3 - x^2$$

$$2x^2 - 3x$$

$$x^2 - 3$$

Q6.
Which of these calculations are the same as $$11 \times 14$$ ?

$$(10 \times 10) + (1\times 4)$$

$$(11\times 7) + (11\times 2)$$

Correct answer: $$(1 \times 14) + (10 \times 14)$$

Correct answer: $$(4\times 11) + (10\times 11)$$

$$(4\times 11) + (1\times 14)$$

Assessment exit quiz

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6 Questions

Q1.
Which of these expressions are binomials?

Correct answer: $$x + 4$$

$$ x^2 + 2x + 2$$

$$2x + 3x$$

Correct answer: $$x - 6$$

$$xy$$

Q2.
Here is an area model for $$(x + 2)(x + 4).$$ Which of these expressions is the correct expanded form?

$$x^2 + 2x + 8$$

$$x^2 + 4x + 4$$

Correct answer: $$x^2 + 6x + 8$$

$$x^2 + 8x + 6$$

$$3x^2 + 4x + 8 $$

Q3.
Here is an area model for $$(x - 3)(x - 1).$$ Which of these is the correct expanded form?

$$x^2 -2x + 3$$

Correct answer: $$x^2 -4x + 3$$

$$x^2 -4x - 3$$

$$x^2 + 4x + 3$$

$$x^2 + 4x - 3$$

Q4.
Which product of two binomials could be represented by this area model?

$$(x - 15)( x - 8)$$

$$(x - 15)( x + 8)$$

$$(x - 10)( x + 12)$$

$$(x + 12)( x - 10)$$

Correct answer: $$(x + 15)( x - 8)$$

Q5.
Which is the correct expanded form of $$(x - 3)^2$$ ?

$$x^2 - 9$$

$$x^2 + 9$$

$$x ^2 - 6x - 9$$

Correct answer: $$x^2 - 6x + 9$$

$$x ^2 + 6x - 9$$

Q6.
Match each product of two binomials to its correct expansion.

Correct Answer:$$(x + 7)(x + 3)$$,$$x^2 + 10x + 21$$

Correct Answer:$$(x + 7)(x - 3)$$,$$x^2 + 4x - 21$$

Correct Answer:$$(x - 7)(x + 3)$$,$$x^2 - 4x - 21$$

Correct Answer:$$(x - 7)(x - 3)$$,$$x^2 - 10x + 21$$

Correct Answer:$$(x + 7)^2$$,$$x^2 + 14x + 49$$

Correct Answer:$$(x - 7)^2$$,$$x^2 - 14x + 49$$

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The product of two binomials

The product of two binomials

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.$$2x$$ and $$5x$$ can be called __________ terms.

Q2.What expression could these algebra tiles represent?

Q3.Which is the correct area model to show the expansion of $$x(x + 3)$$?

Q4.Expand $$x(x + 8)$$.

Q5.Expand $$x(x - 3)$$.

Q6.Which of these calculations are the same as $$11 \times 14$$ ?

Assessment exit quiz

6 Questions

Q1.Which of these expressions are binomials?

Q2.Here is an area model for $$(x + 2)(x + 4).$$ Which of these expressions is the correct expanded form?

Q3.Here is an area model for $$(x - 3)(x - 1).$$ Which of these is the correct expanded form?

Q4.Which product of two binomials could be represented by this area model?

Q5.Which is the correct expanded form of $$(x - 3)^2$$ ?

Q6.Match each product of two binomials to its correct expansion.

Lesson appears in

UnitMaths / Expressions and formulae

Maths

Q1.
$$2x$$ and $$5x$$ can be called __________ terms.

Q2.
What expression could these algebra tiles represent?

Q3.
Which is the correct area model to show the expansion of $$x(x + 3)$$?

Q4.
Expand $$x(x + 8)$$.

Q5.
Expand $$x(x - 3)$$.

Q6.
Which of these calculations are the same as $$11 \times 14$$ ?

Q1.
Which of these expressions are binomials?

Q2.
Here is an area model for $$(x + 2)(x + 4).$$ Which of these expressions is the correct expanded form?

Q3.
Here is an area model for $$(x - 3)(x - 1).$$ Which of these is the correct expanded form?

Q4.
Which product of two binomials could be represented by this area model?

Q5.
Which is the correct expanded form of $$(x - 3)^2$$ ?

Q6.
Match each product of two binomials to its correct expansion.