Question

Multiply and simplify. Assume that all variables represent nonnegative numbers.
(square root 6+3)( square root 6-1)

Answer 1

What an odd thing to say. There are no variables.

What's preventing you from multiplying these binomials?

Can you do these: (x+2)(x-4)?

Answer 2

(square root 9)(square root 5)

Answer 3

What is that? That has nothing to do with either the original problem statement or my inquisitive example. If you show your intermediate steps - your work - we can see where you wander off.

Answer 4

im lost

Answer 5

Okay, answer my question. CAn you multiply these binomials? (x+2)(x-4)

Answer 6

yes

Answer 7

Please demonstrate. Do NOT just write the final result.

Answer 8

x*x= x, 2*4=8

Answer 9

Only two pieces? That is not correct.

Okay, try this. (10 + 3)(10 + 4)

Answer 10

know I can multiply them right

Answer 11

Notice how in multiplying 13 * 14 there are FOUR pieces to consider.

(10 + 3)(10 + 4) = 10*10 + 10*4 + 3*10 + 3*4

Do you see all four of those pieces?

Answer 12

yes

Answer 13

Okay, now to my first question. What are the FOUR pieces of this multiplication?

(x+2)(x-4)

Answer 14

(10*10)(10*4)(3*10)(3*4)

Answer 15

Well, that's a good enough LIST, but it is not a good enough result. They should be connected by addition. Have you met the "Distributive Property"?

Answer 16

yes

Answer 17

That is ALL we are doing, here.

(10 + 3)(10 + 4) = 10(10 + 4) + 3(10 + 4) = 10*10 + 10*4 + 3*10 + 3*4

It's all the Distributive Property - Nothing else.

Answer 18

ok

Answer 19

Okay, let's move on to the other example.

Multiply these. Use the Distributive Property to find the FOUR pieces.

(x+2)(x-4)

Answer 20

(x+2)(x-4)=x(x+2)+2(x-4)=x*x+x*4+2*x+2*4

Answer 21

Not bad, but it is a little confused. Look at this and spot the difference...

(x+2)(x-4) = x(x-4) + 2(x-4) <== See how it is (x-4) both times? This is important.

(x+2)(x-4) = x(x-4) + 2(x-4) = x*x - x*4 + 2*x - 2*4 <== This one is additionally different because I noticed the negative signs. All yours turned into "+"! That's no good.