multiplying squared numbers

[mollykins]

my mind has gone blank and now i can't work out the answer to this simple question. I can't do the squared symbol so ^ means squared in this example, and * means cubed ok.

2x(x^-4), would it be 2x*-8x, or 3x^-8x?????

Please help, my mind has gone blank . . . .

[Prudie]

2x* - 8x (2x cubed - 8x)

[Old_Geezer]

Yeah.

Been a while since I did such homework :-)

I reckon 2x(x²-4)

2x * x² = 2x³
2x * -4 = -8x

So 2x(x²-4) = 2x³ - 8x

[mollykins]

thanks, stuff like that has always confused me.

[Canary42]

You could always check by substituting a number for x and seeing which works out as correct (presuming your arithmetic is superior to your algebra LOL)

[mollykins]

i never thought of doing that . . . .

[factor-fiction]

Agree with the other answers. I'm not clear where the idea of a coefficient of 3 came from.
You simply multiply each term inside the brackets in turn by the term outside teh bracket.
To check an expansion tlike this it's normally easiest to substitute x=1 into the original expression and the expanded expression, then if that works as an extra check use x=2 if you want to be doubly sure.
Ask again if you have any maths questions for us

[Canary42]

Beware using x=1 as substitute, it will give the same answer for all powers of x, e.g. it will validate x=x^

[factor-fiction]

I agree canary - using x=1 is not always appropriate, but it is a good starting point when there is uncertainty as to what the coefficients should be as in mollykins' case. Yes, far better to use something like x=9.5 if your number skills are okay with that but it can get unwieldy, especially for cubes.

[vinginge]

2x (x^-4) = 2x^1(x^-4)
When you multiply numbers with powers/indices/exponents you add the exponents.
So 2x^1(x^-4) = 2x^-3 = 2/x^3 = 2/8 = 1/4.

[vinginge]

My mind also went blank and for some reason I put x = 2.
The answer is 2/x³.