CPhill

Here's another way to do this one, rosala

(l+m)^2 - (l-m)^2

[ (l + m) - (l - m) ] [ (l + m) + (l - m)] =

[2m] [2l ]=

4ml

x^4 - ( x- z)^4 =

[x^2 -(x - z)^2 ] [ x^2 + (x-z)^2 ]=

[x + (x - z)] [x - (x -z)] [ x^2 + x^2 - 2xz + z^2 ] =

[2x - z ] [z ] [2x^2 - 2xz + z^2 ]

We would have to know the angle sum for the three angles

For instance..if the angles summed to 180 degrees

2x  would be larger than [30 + x]

But if the angles summed to 90 degrees

[30 + x] would be larger than 2x

LOL!!!...you're really close to the answer....!!!

Let me see if I can finish for you...

We have

4 [ x^2 - 2x + 1 ] =        square root of x^2 = x     square root of 1 = 1  ... and those are the two things we want to factor with.....!!!

4 (x - 1) (x -1)  =

4(x -1) ^2

Do you see it, now ??

Don't let that lead "4" fool you...we're just letting it ride along.....!!!

18.29 m   = 1829 cm

So dividing  1829 by 30 will give you the answer

OK, rosala......

Remember that the first thing we want to do before we ever start factoring is to take out the common factor  (here it's 4)...so we have

4 [x^2 - 2x +1]   .....now let's just factor the expression in the parentheses...we'll go back and tack on the "4" at the end...

So what's the square root of x^2 ???

And what's the square root of 1  ??

And what sign do we use between the terms??

Let me know if this one gives you trouble....it's a little different...

rosala..is the middle term supposed to be +84yz...???...check it again...

Isnt the problem   49y^2 + 84yz + 36z^2 ??

If so...your final answer is perfect!!!

.....or even falling down the stairs....!!!

This one is known as a "perfect square" trinomial

When the first and last terms are perfect squares (which they are)...always try this factorization..

Take the square root of the first term = 5m   and the square root of the last term = 9

Write them twice separated by a "+" sign

(5m + 3) (5m + 3)   ....notice that when we expand this we get

25m^2 + 15m + 15m + 9   = 25m^2 + 30m + 9....just what we started with...!!

As you improve your factoring skills, these will be easy to recognize....don't worry about it too much if you don't see it right away, right now...!!!

Also...if the middle term had been -30m  we would have just written (5m - 3) (5m - 3) ...

Sorry, Alan....!!!