How do I Simplify this?

Question

10w(Squared) - 4w + 3w(Squared) + 18w

Is it possible for you to show work so I can learn how to do the other problems.

Answer 1

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Multiples same variables raised to the same exponent can be merged to reduce the size of the equation.

In this case, you have two sets: w^2 (or w(squared)) and w

remember that you can rearrange the equation and section it off in certain ways without changing the outcome.

10w^2 - 4w + 3w^2 + 18w

= 10w^2 + 3w^2 + 18w - 4w <--- Putting like terms together

= (10w^2 + 3w^2) + (18w - 4w) <--- sectioning off the terms we're going to combine (remember that you can split addition and subtraction with parenthesis, but multiplication and division would have to be factored)

= 13w^2 + 14w <--- combining like terms.

If your wondering why this works, the easiest way to see that this works is to substitute numbers for w.

let's try 1

if w = 1, then

10w^2 - 4w + 3w^2 + 18w = 10*1 - 4*1 + 3*1 +18*1 = 10 - 4 + 3 + 18 = 27

10w^2 + 3w^2 + 18w - 4w = 10*1 + 3*1 + 18*1 - 4*1 = 10 + 3 + 18 - 4 = 27

(10w^2 + 3w^2) + (18w - 4w) = (10*1 + 3*1) + (18*1 - 4*1) = (10+3)+(18-4) = 13+14 = 27

13w^2 + 14w = 13*1 + 14*1 = 13+14 = 27

You see that add multiples of the same variable works at every step.

Let's try it again with 2, so that you can see that it works with exponents

10w^2 - 4w + 3w^2 + 18w = 10*4 - 4*2 + 3*4 +18*2 = 40 - 8 + 12 + 36 = 80

10w^2 + 3w^2 + 18w - 4w = 10*4 + 3*4 + 18*2 - 4*2 = 40 + 12 + 36 - 8 = 80

(10w^2 + 3w^2) + (18w - 4w) = (10*4 + 3*4) + (18*2 - 4*2) = (40+12)+(36-8) = 52+28 = 80

13w^2 + 14w = 13*4 + 14*2 = 52+28 = 80

Another way to view it is that multiplication is essentially the addition of the same number repeated a certain number of times. e.g. 3x = x + x + x

so.. 18w - 4w = w + w + w + w + w + w + w + w + w + w + w + w + w + w + w + w + w + w - (w + w + w + w)

= w + w + w + w + w + w + w + w + w + w + w + w + w + w + w + w + w + w - w - w - w - w <-- distribute the negative.

= w + w + w + w + w + w + w + w + w + w + w + w + w + w + (w - w) + (w - w) + (w - w) + (w - w) <-- resection

= w + w + w + w + w + w + w + w + w + w + w + w + w + w + 0 + 0 + 0 + 0

=14w

w^2 is usually going to be a different number than w (the obvious exceptions being 1 and 0), so w^2 has to be treated as a different number when you're simplifying.

Answer 2

10w^2-4w+3w^2+18w

combine similar terms (10w^2 +3w^2)

13w^2 +14w is the simplified answer

Answer 3

10w^2 - 4w + 3w^2 + 18w

1. you will just combine like-terms

10w^2 - 3w^2= 7w^2 (all i did ws subtract)

4w - 18w = -14w

2. your final answer is......7w^2-14w :-)