How do you distribute with an exponent on the parenthesised term? For example, 2(x+1)^2?

Question

It's all in the question basically...how would you distribute something like this:

2(x+1)^2

Or this:
1/2(x+4)^2

An explanation would be very helpful. Thanks a bunch...
-Tom

Answer 1

You have to think of this as a multiplication of the item in parentheses. And the exponent tells you how many times.

For example:
2(x+1)²

2(x+1)(x+1)

Now you just multiply using FOIL (first, outer, inner, last)
First terms (x and x) --> x * x = x²
Outer terms (x and 1) --> x * 1 = x
Inner terms (1 and x) --> 1 * x = x
Last terms (1 and 1) --> 1 * 1 = 1

So (x + 1)(x + 1) = x² + 2x + 1

Thus 2(x+1)² = 2x² + 4x + 2

The second example is similar:
(x+4)² = (x+4)(x+4)

= x² + 8x + 16

Then multiplying by 1/2 gives:
(1/2)x² + 4x + 8

Answer 2

First one:
two times the parentheses squared
2 (x+1)(x+1) = 2 (x^2 + 2x + 1) = 2 x^2 + 4x + 2

one half times the parentheses squared
1/2 (x+4)(x+4) = 1/2 (x^2 + 8x + 16) = 1/2 x^2 + 4x + 8
or (x^2)/2 + 4x + 8

Answer 3

More than using the term "distribute" I recommend you to say develop the expression.Both of them are instances of the Binomial theorem. But in this case seeing that exponential is of low degree (is 2) we can develop it more extensely as follows in order to understand:

You can develop the first instance as follows:

2(x+1)² = 2(x+1)(x+1) = 2[x²+x+x+1²] =
=2 [x²+2x+1²] = 2x²+4x+2

The second one is as follows:

1/2(x+4)² -- (the only diference with the above is that binomial is denominator of a fraction)

1/2(x+4)² = 1 / 2[x²+8x+4²] = 1/[2x²+16x+16]

That's it!

Good luck!

Answer 4

Good question! If you are not sure how it would be understood by answerers, then use parentheses, the more the better! Use also spaces.
2(x+1)^2 is clear! a=x+1, then b=a*a, then c=2*b;
1/2(x+4)^2 is doubtful! Either 1/{2*(x+4)^2} or (1/2)*(x+4)^2 ???

and read you own question once more before sending it

Answer 5

Think what exponentiation is. It is the repeated multiplication of a thing by itself. Therefore, expanding (something)^2 gives something * something. It is quite simple if you understand what the operations mean. So

2(x+1)^2 = 2*(x+1)*(x+1) = 2*(x^2 + 2x + 1) = 2 x^2 + 4x + 2

Answer 6

ok u have to use the equation (a+b)^2=a^2+b^2+2ab
so the first one would be 2(x^2+1+2x)=2X^2+4x+2
and the second one would be 1/2(x^2+16+8x)=1/2x^2+4x+8

Answer 7

unique situation: x2 (exponent) 6x-2x-12 assemble like words (something the comparable): x2 4x-12 x2= x-12 answer: x-12 tha'ts as much as i will help desire its surprising sorry if its not!:)

Answer 8

I was taught the mnemonic Pretty Please My Dear Aunt Sally.

Meaning:
Powers
Parentheses
Multiply
Divide
Add
Subtract

In your first case, you would do the powers (the square term):
(x+1)^2=x^2+2x+1
And then multiply:
2(x^2+2x+1)=2x^2+4x+2