Question

What is (x^2+1) times (2x)

Answer 1

distribute

(a+b) x (c) = (a x c) + (b x c)

Answer 2

So
(x^2 (times) 2x) + (1 (times) 2x)

Answer 3

That's right

Answer 4

Well I don't know what the first half would be. I don't know how to do the x's
So it's something + 2x

Answer 5

ok well your almost there

Answer 6

\[An^p\times Bn^q=(A\times B)\times n^{p+q} \]

Answer 7

2x^3?

Answer 8

YES!

Answer 9

Well that's what I thought it was but it's not one of my choices...

Answer 10

what was your final answer?

Answer 11

2x^3 + 2x

Answer 12

Hmm, that is right,

what are the choices?

Answer 13

2x^2 +2
2x^2+1
x^2+4x+4
4x^2+1

Answer 14

Are you sure those are the right options for this question?

Answer 15

Yepp. Here I'll put the whole question here so you can see if I'm trying to do this wrong.

Answer 16

ah i see the propbem

Answer 17

you have found
the product of the functions
\[(f\cdot g)(x)=f(x)\times g(x)\]

the question is looking for the function of a fcunction
\[[f\circ g](x)=f\big(g(x)\big)\]

Answer 18

*function of a function.

Answer 19

\[f(x)=x^2+1\\g(x)=2x\\
\\
[f\circ g](x)=f\big(g(x)\big)=f(2x)=(2x)^2+1=\]

Answer 20

\[[g\circ g](x)=g\big(g(x)\big)=g(2x)=2(2x)=4x\]

Answer 21

have you seen this notation before?

Answer 22

@RoseDryer

Answer 23

are you still here?

Answer 24

I'm sorry I was making a bottle.

Answer 25

I have not seen that before

Answer 26

does it make any sense ?

Answer 27

So it would be f(g(x))

Answer 28

yeah

Answer 29

So (2x)^2+1

Answer 30

yes, last step is to simplify that

Answer 31

How do I?

Answer 32

\[(2x)^2=(2x)\times(2x)=(2\times2)(x\times x)=\]

Answer 33

So 4x^2?

Answer 34

yep

Answer 35

so your final answer now is ____ _ _

Answer 36

yep

Answer 37

4x^2+1

Answer 38

Correct \[\boxed{\large\color{red}\checkmark}%unk\]

Answer 39

do you want another simple example with this new notation?

Answer 40

I just want to know why we simplified.

Answer 41

do you when we simplified (2x)^2 ?

Answer 42

What?

Answer 43

do you mean* when we simplified (2x)^2 ?

Answer 44

Yeah. Why did we have to do that?

Answer 45

we did that because our final answer is a quadratic, and a nice general for of a quadratic is

ax^2+bx+c=0

where a, b, c are the coefficeints,

we simplified to get the coefficent next to the x^2 term

Answer 46

Ahh. Okay

Answer 47

if (2x)^2+1 was an option that would be correct as well.

Answer 48

It is.

Answer 49

\(2x^2\) is different to \((2x)^2\)

Answer 50

Oh okay.