The product of two binomials | Maths | Quizalize & Oak National Academy

Starter quiz

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

equivalent

identical

inverse

like ✓

reciprocal
What expression could these algebra tiles represent?

$x^2 + 6x + 9$ ✓

$6x^2 + 9$

$7x + 9$

$4x^2 + 9x$

$x^2 + 15x$
Which is the correct area model to show the expansion of $x(x + 3)$ ?
Expand $x(x + 8)$ .

$2x + 8$

$10x$

$9x^2$

$x^2 + 8$

$x^2 + 8x$ ✓
Expand $x(x - 3)$ .

$x^2 + 3x$

$x^2 - 3x$ ✓

$3 - x^2$

$2x^2 - 3x$

$x^2 - 3$
Which of these calculations are the same as $11 \times 14$ ?

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

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

$(1 \times 14) + (10 \times 14)$ ✓

$(4\times 11) + (10\times 11)$ ✓

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

Exit quiz

Which of these expressions are binomials?

$x + 4$ ✓

$x^2 + 2x + 2$

$2x + 3x$

$x - 6$ ✓

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

$x^2 + 2x + 8$

$x^2 + 4x + 4$

$x^2 + 6x + 8$ ✓

$x^2 + 8x + 6$

$3x^2 + 4x + 8$
Here is an area model for $(x - 3)(x - 1).$ Which of these is the correct expanded form?

$x^2 -2x + 3$

$x^2 -4x + 3$ ✓

$x^2 -4x - 3$

$x^2 + 4x + 3$

$x^2 + 4x - 3$
Which product of two binomials could be represented by this area model?

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

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

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

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

$(x + 15)( x - 8)$ ✓
Which is the correct expanded form of $(x - 3)^2$ ?

$x^2 - 9$

$x^2 + 9$

$x ^2 - 6x - 9$

$x^2 - 6x + 9$ ✓

$x ^2 + 6x - 9$
Match each product of two binomials to its correct expansion.

$(x + 7)(x + 3)$

⇔

$x^2 + 10x + 21$ ✓

$(x + 7)(x - 3)$

⇔

$x^2 + 4x - 21$ ✓

$(x - 7)(x + 3)$

⇔

$x^2 - 4x - 21$ ✓

$(x - 7)(x - 3)$

⇔

$x^2 - 10x + 21$ ✓

$(x + 7)^2$

⇔

$x^2 + 14x + 49$ ✓

$(x - 7)^2$

⇔

$x^2 - 14x + 49$ ✓

Worksheet

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Video

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.

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.

Keywords

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