Factorising expressions | Maths | Quizalize & Oak National Academy

Starter quiz

$1, 2, 3, 6, z, 2z, 3z$ and $6z$ are __________ of $18yz$ and $24xz$

common factors ✓

products

common multipliers

variables
List all the factors of $7xy$

$7, x, y$

$7, 7x, 7y$

$7, 7x, 7y, 7xy$

$1, 7, 7x, 7y, 7xy$

$1, 7, x, 7x, y, 7y, xy, 7xy$ ✓
Which is not a factor pair for $30ab^2c$ ?

$3ab \times 10bc$

$2ab \times 15bc$

$2abc \times 15bc$ ✓

$abc \times 30b$

$b^2 \times 30ac$
List the common factors of $5cd$ and $35de$

$1, 5, d, 5d$ ✓

$1, 5$

$d, 5d$

$1, 5d$

$35cde, 70cde, 105cde...$
Find the highest common factor of the terms $8ab$ and $20b^2$

$b$

$2$

$2b$

$4b$ ✓

$4$
Find the HCF of the terms in the expression $6d^3e^2f -8d^2ef^2+10d^3e$

$6d^2e$

$4d^2e$

$2d^2e$ ✓

$2de$

$2d^2$

To __________ is to express a term as a product of its factors.

multiply

expand

factorise ✓

simplify
Which of the below factorises the expression $10x+20$

$2(5x+10)$ ✓

$10(x+2)$ ✓

$5(2x+4)$ ✓

$10(x+20)$

$8x+16+2x+4$
Match the expressions to their factorised form.

$3e+9$

⇔

$3(e+3)$ ✓

$9-3e$

⇔

$3(3-e)$ ✓

$-3e-9$

⇔

$-3(e+3)$ ✓

$3e^2+9$

⇔

$3(e^2+3)$ ✓

$3e^2+9e$

⇔

$3e(e+3)$ ✓
The difference between $2(5y+15)$ and $10(y+3)$ is that the latter is ______ factorised.

'fully' ✓
Which of the below is not fully factorised?

$6(3x-y)$

$3(6x-y)$

$6y(3x-y)$

$6y(3x-xy)$ ✓

$6(3x-y-3)$
Factorise $-6a^2b^3d-39a^3b^4cd$

$3ab^2d(-2ab-13a^2b^2c)$ ✓

$3ab^2d(-2abd-13a^2b^2cd)$

$-3ab^2d(2ab+13a^2b^2c)$ ✓

$3ab^2d(-2ab-13a^2b^3c)$

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2(3y+9) is not factorised.

It is factorised; just not fully. The distinction is important as sometimes it can be beneficial to not fully factorise.

Factorise - To factorise is to express a term as the product of its factors.
Fully factorise - To fully factorise is to factorise to the point that remaining term or terms cannot be factorised any further.