What to do first? Example: 2x(x+1)(x-1)?

Question

Would you distribute inside parenthesis first or outside to inside...I am so confused about these...

so would it be like...
2x(xsquared-1x+1x-1)
2x(xsquared-1)
2xsquared-2x
?

Answer 1

I've seen textbooks do it different ways. It actually doesn't matter in the example you've provided. See, it can be written:

(2x)(x+1)(x-1)

If you do the 2x(x+1) first, then multiply it by the (x-1), it will give you the same answer as doing the (x+1)(x-1) first then multiplying it by the 2x afterwards. That's because it doesn't matter which order you do multiplications in. 4 x 5 x 3 is the same as 3 x 4 x 5.

This is not the same as PEDMAS or BEDMAS, which gives you the order of operations. The P/B for "parentheses" or "brackets" refers to working out the math required INSIDE the parentheses. You have no math to work out inside the parentheses in the example you provided.

ADDED: Just to prove it since others are giving the answer the other way:

2x(x+1)(x-1)
=(2x^2 + 2x)(x-1)
=2x^3 - 2x^2 + 2x^2 - 2x
=2x^3 - 1

You also have something present in your example called the Difference of Squares. Is that something you've heard before? If so, then the examples everyone is providing would be more reflective of what your teacher would want. The difference of squares is when you have things like (x+1)(x-1), or (x+2)(x-2). There's a specific pattern to make solving easier. The Difference of Squares means that the lone x's get cancelled out, so you are just left with the square of the variable (x) minus the square of the constant (1, in your case).

For the further information you've added, remember that your 2x times your x-squared gives you 2x-cubed.

Answer 2

its doesn't matter which you multiply first, associative property of multiplication.

i would do the 2 parenthesis first and get (2x)x^2 - 1
then u muliply it and get 2x^3 - 2x

under ur additional details u messed up on the last two steps: multiplying 2x and xsquared gives u 2xcubed because now u hav 3x's

Answer 3

First, I would multiply the 2x by everything in the first set of parenthesis (x+1). -----> (2xsquared + 2)... then multiply everything in the parenthesis (2xsquared +1)(x-1). 2xsquared by x, 2xsquared by -1, etc...You should get this:
2xcubed - 2xsquared + 2x - 2.

Answer 4

2x(x+1)(x-1)
=2x(x^2-1)
=2x^3-2x

Answer 5

2x(x+1)(x-1)
=2x(x^2-1)
=2x^3-2x

Answer 6

Always do what's in parenthesis first!

Answer 7

2x(x+1)(x-1)
2x(x^2-1)
2x^3-2x