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More complex binomial products

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Lesson details

Learning outcome

I can find more complex binomial products.

Key learning points

  1. The coefficients of the variable(s) may not be one.
  2. Sometimes the terms within each binomial are not in the same order.
  3. Multiplication and addition/subtraction with negative numbers is useful here.

Keywords

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

Common misconception

Mistakes with partial products are even more common where algebraic terms in the binomials have coefficients greater than 1. It is common to find pupils writing that the product of 2x and 3x is 5x

Reminding pupils that because multiplication is commutative the product of 2x and 3x can be thought of as 2 × 3 × x × x

Teacher tip

Pupils can re-order the terms in the binomial to have algebraic terms first but with the area model it isn't necessary so pupils should ensure they are comfortable and accurate with their chosen approach.

Licence

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).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
Which of these expressions are binomials?

Correct answer: $$x - 8$$
Correct answer: $$2a + 4$$
$$x^2 + 4x + 4$$
Correct answer: $$3y - 2x$$
$$2xy$$

Q2.
Which of these are equivalent to $$a - 6$$ ?

$$6 - a$$
$$-a + 6$$
Correct answer: $$-6 + a$$
$$-6a$$

Q3.
In the expression $$6x + 4$$, you call 6 the of $$x$$.

Correct Answer: coefficient

Q4.
Match each product to its simplified form.

Correct Answer:$$x \times -x$$,$$-x^2$$

$$-x^2$$

Correct Answer:$$-x\times -x$$,$$x^2$$

$$x^2$$

Correct Answer:$$-2x \times -3x$$,$$6x^2$$

$$6x^2$$

Correct Answer:$$-6x \times y$$,$$-6xy$$

$$-6xy$$

Correct Answer:$$-3y \times -2x$$,$$6xy$$

$$6xy$$

Correct Answer:$$6x\times -x$$,$$-6x^2$$

$$-6x^2$$

Q5.
Which of these expressions can be written as the difference of two squares?

$$(x-29)^2$$
$$(x + 29)(x - 20)$$
Correct answer: $$(x + 29)(x - 29)$$
$$(x - 9)(x - 9)$$
$$(x - 9)(y + 9)$$

Q6.
Match each product of two binomials to its expanded form.

Correct Answer:$$(x - 5)^2$$,$$x^2 - 10x + 25$$

$$x^2 - 10x + 25$$

Correct Answer:$$(x - 4)(x - 6)$$,$$x^2 - 10x + 24$$

$$x^2 - 10x + 24$$

Correct Answer:$$(x + 2)(x - 12)$$,$$x^2 - 10x - 24$$

$$x^2 - 10x - 24$$

Correct Answer:$$(x + 4)(x - 6)$$,$$x^2 - 2x - 24$$

$$x^2 - 2x - 24$$

Correct Answer:$$(x + 4)(x + 6)$$,$$x^2 + 10x + 24$$

$$x^2 + 10x + 24$$

Correct Answer:$$(x + 12)(x - 2)$$,$$x^2 + 10x - 24$$

$$x^2 + 10x - 24$$

Assessment exit quiz

Download exit quiz questions (PDF)

6 Questions

Q1.
Which binomial expression is equivalent to $$8 - x$$ ?

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

Q2.
Which product of two binomials is equivalent to $$(x - 5)(5 - x)$$ ?

$$(x - 5)^2$$
$$(5 - x)^2$$
$$(x - 5)(-x -5)$$
Correct answer: $$(x - 5)(-x + 5)$$
Correct answer: $$(5 - x)( -5 + x)$$

Q3.
Which of these expressions can be written as the difference of two squares?

$$(a - b)(b - a)$$
Correct answer: $$(1 - a)(a + 1)$$
Correct answer: $$(a - b)(-b - a)$$
$$(6 - b)(-b + 6)$$
$$(a - 4)(4 + b)$$

Q4.
Match each product of two binomials to its expanded form.

Correct Answer:$$(x + 4)(4 -x)$$,$$-x^2 +16$$

$$-x^2 +16$$

Correct Answer:$$(x - 4)(4 -x)$$,$$-x^2 +8x -16$$

$$-x^2 +8x -16$$

Correct Answer:$$(x - 4)(4 + x)$$,$$x^2 -16$$

$$x^2 -16$$

Correct Answer:$$(x - 4)(-4 +x)$$,$$x^2 - 8x + 16$$

$$x^2 - 8x + 16$$

Q5.
$$(3x -1)(2x + 5)$$ can be expanded and simplified to give $$6x^2 +$$ $$x - 5$$.

Correct Answer: 13, +13

Q6.
Expand and simplify $$(2b - 3a)(2a - 3b)$$.

$$-6a^2 -5ab-6b^2$$
$$5ab-6a^2-6b^2$$
$$6a^2 +6b^2-13ab$$
$$6b^2-6a^2-5ab$$
Correct answer: $$13ab-6b^2-6a^2$$

To help you plan your 9 maths lesson on: More complex binomial products, download all teaching resources for free and adapt to suit your pupils' needs...