seeking a math genious, math teacher to help me understand this question,?

Question

(s-2t)^2-4w^2
Please explain the steps thank you!

Answer 1

(s - 2t)^2 - 4w^2
= (s-2t) (s-2t) - 4w^2
= s^2- 2st- 2st+ 4t^2 - 4w^2
= s^2 -4st +4t^2 - 4w^2
it is just like saying 4^2 = 4x4=16
then you solve.
if the question says w^2 -100
then your answer will be (w + 10) ( w- 10)
if you notice the question i used has an example doesnt have a bracket

Answer 2

Well, Looks like you should simplify the expression. What that means is, there is a "simpler" way of re-writing that expression that you provided. The definition of "simpler" is quite subjective (take it from a prospective teacher). What is most likely expected of you is to perform the operations to manipulate the expression.

Without some sort of context, it is difficult to say which way of writing the expression is correct.

So here's what I would do:
(s-2t)^2 - 4w^2
=(s - 2t)*(s - 2t) - 4w^2 [definition of (...)^2]
=(s^2 - 2st - 2st + 4t^2) - 4w^2 [distributive property, a.k.a. "FOIL")
= s^2 - 4st + 4t^2 - 4w^2 [all the ()'s drop off because all the terms are added/subtracted]
= s^2 + 4(-st + t^2 - w^2) [this is called factoring out the 4; notice if you used the distributive property that this expression is equal to the previous one. Notice I kept the 4 positive. If I wanted the 4 to be negative, then would get:
s^2 - 4(st - t^2 + w^2)

This is as far as I can go as far as simplifying because the terms are all different.

Answer 3

Did your "question" include any instructions? I would understand the question better myself if I knew what I was instructed to do with the given expression.

My guess is that you are asked to either factor or expand the expression. If factoring is requested, then it is simply a matter of factoring the difference of squares.

x² - y² = (x + y)(x - y)

Let x = s - 2t and let y = 2w ← (why 2w and not 4w?)

(s-2t)² - (2w)²

= ([s - 2t] + 2w)([s - 2t] - 2w)

= (s - 2t + 2w)(s - 2t - 2w)

If you are asked to expand the expression, then you have

(s-2t)² - (2w)²

= (s-2t)(s-2t) - 4w²

= s² - 2st - 2st + 4t² - 4w²

= s² - 4st + 4t² - 4w²

I hope this or one of the other answers help you to better understand your question.

Answer 4

1.)write (S-2t)^2 two times like this; (S-2t)(S-2t)- 4w^2
2.) Foil and you should get S^2 - 2tS - 2Ts + 4t^2 - 4w^2.
3.) simplify the polynomial to: S^2 - 4tS + 4t^2 - 4w^2
4.) Write in descending order: S^2 +4t^2 - 4w^2 - 4ts doesn't matter which ^2 comes first as long as it's descending.)
5.) Your polynomial should be solved now.

Answer 5

What's the quetion - expression is just an expression. Nothing to do with it except expand (s-2t)^2 = s2 - 4t + 4t^2, then include -4w^2

Answer 6

This is a very simple question and to factorise it you have just to follow the formula of identity a^2-b^2=(a+b)(a-b)
(s-2t)^2-4w^2
=(s-2t)^2-(2w)^2 [4w^2 is converted to(2w)^2]
=(s-2t+2w)(s-2t-2w)

Answer 7

For factoring the expression:

We can rewrite 4w^2 as: (2w)^2.
Notice that you now have a difference of two squares. In general:
a^2-b^2 = (a+b)(a-b).

So, in our case, a = s-2t, and b = 2w. Thus:
(s-2t)^2-(2w)^2
= ((s-2t)+(2w))((s-2t)-(2w))
= (s-2t+w2)(s-2t-2w)

Answer 8

(s-2t)^2-4w^2

Look at this as a form of X^2 -Y^2
This factors into X-Y and X+Y

In your problem the "X" is (s-2t)
and the "Y" is 2w

so the factors are (s-2t)-2 and (s-2t) +2W
s-2t-2w and s - 2t +2w

Answer 9

enable d = the style of canines enable b = the style of boys we can write equations. First, write one for this sentence: there have been 40 heads in all. each and every canines and each boy has in basic terms a million head, suited? d + b = 40 Write one for this one: there have been an entire of one hundred ft. each and every canines has 4 ft, so as that's 4d and each boy has 2 ft, so as that's 2b. 4d + 2b = one hundred d + b = 40 4d + 2b = one hundred -2(d + b = 40) 4d + 2b = one hundred -2d - 2b = -eighty -------------------- 2d = 20 d = 10 b + d = 40 b + 10 = 40 b = 30 there have been 10 canines and 30 boys. examine it. each and every canines has 4 ft, so as that's 40 ft. and each boy has 2 ft, so as that's 60 ft. 60 + 40 = one hundred, examine! and each canines has a million head, so as that's 10 heads. and each boy has a million head, so as that's 30 heads. 30 + 10 = 40, examine!

Answer 10

Remember this basic factor?
(x^2-y^2)=(x+y)(x-y)
That's how we start out.

(s-2t)^2-4w^2

((s-2t)+2w)((s-2t)-2w))

(s-2t+2w)(s-2t-2w)

(s-2(t-w))(s-2(t+w))

Now factor out (s-2)

(s-2)(t-w)(t+w)

Q.E.D.
.