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.