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[ally1784]

Can someone show me the working out for these 2 questions, using this formula.

[p0kem0n21]

Can someone show me the working out for these 2 questions, using this formula.

We should break this up into a few steps. The first step is to manipulate the difference of squares formula to make these expressions easier to expand, and the second step is just expanding correctly! I'd just like to mention how we are trying to write expressions as (a-b)(a+b), and I'll try to apply this simple example to the questions you've presented. For expansion, we want to rewrite this as a² - b².

The first expression is (3w-4z+u)(3w+4z-u). One key thing we should notice here is that 3w is 'shared' between the two factors, whereas the 4z and u have opposite signs in both brackets. This should lead us to believe that 3w can be 'a' (from the example above). Meanwhile, we have 4z-u and -4z+u. One thing to note is that -(4z-u)=-4z+u, which is significant when we realize that we need a 'b' and '-b' (once again, as in the example above). With this knowledge, we can then write the expression as (3w-(4z-u))(3w+(4z-u)), which matches our example expression of (a-b)(a+b). Cool! That's the hardest step done. Now we just expand to get (3w)² - (4z-u)², and expanding again, we get 9w²-16z²-u²+8uz.

Since we are dealing with square roots in the second question and I don't have a root symbol to write with (lol), I'm just going to write rt5 (meaning square root of 5).

Now we have to apply the same two steps to this question. Something here to notice is that both 2a and c are 'shared' between the factors. In other words, we probably do not want to manipulate them. Meanwhile, we have a b*rt5 and -b*rt5. This actually makes our job quite simple. We can rewrite the expression as ((2a+c)-b*rt5)((2a+c)+b*rt5). Expanding this as a difference of squares expression, we get (2a+c)²-(b*rt5)² (and then 4a²+4ac+c²-5b²).

[ally1784]

How do you factorise this?

[p0kem0n21]

How do you factorise this?

Hey, I recommend asking short questions like these on the respective threads, such as the VCE Methods Question Thread (just a piece of advice, you'll probably get answers sooner).

Anyways, this factorisation question is relatively simple, so I'll try and give you a hint instead. And that is, look for common terms! To give you some sense of direction, try factorising that x² out of x²y²-x² and see what you have in your brackets. Then look at the unfactorised part of the expression and try to see how that compares to what's in your brackets