Checking and securing understanding of the product of two binomials | Maths

Starter quiz

What is the value of $x$ for $3x + 5 = 2(x - 2)$ ?

'-9' ✓
What is the value of $x$ for $\frac{5x + 15}{3} = \frac{2x - 2}{2}$ ?

'-9' ✓
What is the positive value of $x$ for $x^2 - 4x - 12 = 0$ ?

'6' ✓
Rearrange for $x$ : $3y - x = 15$ ?

$x = 3y + 15$

$x = 15 - 3y$

$x = 3y - 15$ ✓
Make $b$ the subject for $a + 2b = 10$

$b = \frac{10-a}{2}$ ✓

$b = \frac{a-10}{2}$

$b = \frac{a}{20}$
Make $p$ the subject of $\frac{2p + q}{3} = 4$

$p = 4 - \frac{q}{3}$

$p = 6 - \frac{q}{2}$ ✓

$p = 2q + 12$

Exit quiz

Expand and simplify the expression: $(x + 3)(x - 2)$

$x^2 - x + 6$

$x^2 + x - 6$ ✓

$x^2 + 5x - 6$
Expand and simplify the expression: $2(x - 1)(x + 5)$

$2x^2 + 10x - 2$

$2x^2 - 10x + 10$

$2x^2 + 8x - 10$ ✓
Expand and simplify the expression: $3(x + 2)^2$

$3x^2 + 12x + 12$ ✓

$3x^2 + 6x + 6$

$3x^2 + 12x + 36$
Expand and simplify the expression: $(2x - 3)(x + 4)$

$2x^2 + 8x - 12$

$2x^2 - x - 12$

$2x^2 + 5x - 12$ ✓
Expand and simplify the expression: $-x(2x - 5)(3x + 1)$

$-6x^3 - x^2 + 5x$

$-6x^3 + 13x^2 + 5x$ ✓

$-6x^3 + x^2 - 5x$
Expand and simplify the expression: $4(y + 3)(2y - 3)$

$8y^2 - 36$

$8y^2 + 12y - 36$ ✓

$8y^2 - 12y - 36$

Worksheet

Loading worksheet ...

Presentation

Loading presentation ...

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.

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)

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.