Question: Factorize: 1) \( k + 6fh + 3f + 3kh \) Expand: 2) \( (2n + 1)^2 \) 3) Make \( V \) the…

Factorize:

1. \( k + 6fh + 3f + 3kh \) Expand:

2. \( (2n + 1)^2 \)

3. Make \( V \) the subject of formula in \( K = \frac{1}{2}(V + 1) \).

The formula \( C = 180n + 450 \) gives the weekly cost \( C \) of running a household of \( n \) people.

4. Find the weekly cost of free people.

5. How many people are there if the weekly cost is \( 1170 \)?

Solution

Problem 1: Expand \( k + 6h + 3t + 2kh \) This expression is already in its expanded form. --- Problem 2: Expand \( (2n + 1)^2 \) \[ (2n + 1)^2 = (2n)^2 + 2 \times 2n \times 1 + 1^2 & \] \[ = 4n^2 + 4n + 1 & \] --- Problem 3a: Make \( V \) the subject of the formula \( k = \frac{1}{2}(v + u)t \) \[ k = \frac{1}{2}(v + u)t & \] \[ 2k = (v + u)t & \] \[ \frac{2k}{t} = v + u & \] \[ v = \frac{2k}{t} - u & \] --- Problem 3b: Given \( C = 180n + 450 \), which gives the weekly cost in dollars of running a household of \( n \) people --- Problem 4: Find the weekly cost for three people \[ C = 180n + 450 & \] \[ C = 180 \times 3 + 450 & \] \[ C = 540 + 450 & \] \[ C = 990 & \] The weekly cost for three people is \$990. --- Problem 5: How many people are there if the weekly cost is \$1170? \[ C = 180n + 450 & \] \[ 1170 = 180n + 450 & \] \[ 1170 - 450 = 180n & \] \[ 720 = 180n & \] \[ n = \frac{720}{180} & \] \[ n = 4 & \] There are 4 people.