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

Starter quiz

Make $x$ the subject of $4x - 3y = 12$

$x = 3y + 12$

$x = \frac{12 + 3y}{2}$

$x = \frac{12 + 3y}{4}$ ✓
Make $p$ the subject of $\frac{p}{2} + q = 7$

$p = -2(q - 3.5)$

$p = -q - 7$

$p = 2(7-q)$ ✓
Make $a$ the subject of $3a -\frac{b}{4} + 2 = 0$

$a = \frac{b - 4 }{12}$

$a = \frac{b - 8 }{4}$

$a = \frac{b - 8 }{12}$ ✓
Expand and simplify the expression: $(x + 3)(x - 2)$

$x^2 + 2x - 6$

$x^2 - x + 6$

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

$2x^2 + 4x - 30$

$2x^2 + 2x - 30$ ✓

$x^2 + 2x - 15$
Expand and simplify the expression: $x(x+5)(x-2)$

$x^3 + 3x^2 - 10x$ ✓

$x^3 + 5x^2 - 10x$

$2x^2+ 3x +10$

Exit quiz

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

$x^3 - x^2 - 14x + 24$

$x^3 + 3x^2 - 2x - 24$

$x^3 - 3x^2 + 10x + 24$

$x^3 + 3x^2 - 10x - 24$ ✓
Expand and simplify the expression: $(2x - 1)(x + 5)(3x - 2)$

$6x^3 + 23x^2 - 33x + 10$ ✓

$6x^3 + 27x^2 + 7x - 10$

$6x^3 - 23x^2 + 33x + 10$

$6x^3 - 29x^2 + 13x + 10$
Expand and simplify the expression: $(y - 2)(2y + 3)(y - 4)$

$2y^3 - 3y^2 - 14y + 24$

$2y^3 - 9y^2 - 2y + 24$ ✓

$2y^3 + 5y^2 - 8y - 24$

$2y^3 - 5y^2 + 14y - 24$
Expand and simplify the expression: $(3x + 1)(x - 2)(4x + 5)$

$12x^3 + 7x^2 - 33x - 10$

$12x^3 - 5x^2 - 33x - 10$ ✓

$12x^3 - 11x^2 + 3x + 10$
Expand and simplify the expression: $(2y - 3)(y + 4)(y - 5)$

$2y^3 - 3y^2 - 23y + 60$

$2y^3 + y^2 - 27y - 60$

$2y^3 - 5y^2 - 37y + 60$ ✓
Expand and simplify the expression: $(2x + 1)(3x - 2)(x - 4)$

$6x^3 - 17x^2 + 8x + 8$

$6x^3 - 25x^2 - 8x + 2$

$6x^3 - 25x^2 + 2x + 8$ ✓

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Lesson Details

Key learning points

The distributive law can be used to find the product of three (or more) binomials.
This can be done by finding the product of two of the binomials first.
The commutative law allows you to choose which two of the binomial expressions to find the product of first.
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.