Question

mpmip - culminating task
task 5: climbing the tower!!
now in pisa, your next challenge is to climb to the top of the leaning
tower of pisa. as you ascend you must answer the question on every
succeeding floor in the tower (there are eight floors in total) to show there
may be some possible answers given. in the space provided, show
your calculations to determine which of the solution is correct. once
you have the correct solution, move on to the next floor of the tower.
dont forget to enjoy the view.

floor	question	show your work	possible answers
4	expand and simplify<br>(2 marks)<br>(3x + 4)(3x - 4)		□ ( 6x^2 + 8x - 16 )<br>□ ( 6x^2 + 24x - 16 )<br>□ ( 9x^2 - 16 )<br>□ ( 9x - 8 )
6	factor fully<br>(2 marks)<br>( x^2 - 9x + 18 )		□ ( (x + 6)(x + 3) )<br>□ ( (x - 6)(x - 3) )<br>□ ( (x - 2)(x - 9) )<br>□ ( (x + 2)(x + 9) )
8	factor fully<br>(3 marks)<br>( (2x^2 - 32) )		no possible solution<br>given. you must<br>calculate this one on<br>your own.

congratulations!!! you have successfully climbed the leaning tower of p
and can now proceed to rome.

Explanation:

Step1: Expand using distributive property

$(x + 4)(x - 6) = x(x-6) + 4(x-6)$
$= x^2 -6x +4x -24$

Step2: Combine like terms

$x^2 + (-6x+4x) -24 = x^2 -2x -24$

Step3: Use difference of squares rule

$(3x + 4)(3x - 4) = (3x)^2 - (4)^2$
$= 9x^2 -16$

Step4: Find factors of 18 that sum to -9

We need two numbers that multiply to $1\times18=18$ and add to $-9$: $-3$ and $-6$.
$x^2 -9x +18 = (x-3)(x-6)$

Step5: Factor out GCF first

$2x^2 -32 = 2(x^2 -16)$

Step6: Factor difference of squares

$2(x^2 -16) = 2(x-4)(x+4)$

Answer:

Floor 2: $\boldsymbol{x^2 - 2x - 24}$
Floor 4: $\boldsymbol{9x^2 - 16}$
Floor 6: $\boldsymbol{(x - 6)(x - 3)}$
Floor 8: $\boldsymbol{2(x - 4)(x + 4)}$