Question

How do you expand a polynomial

Answer 1

erm sorry-

Answer 2

Give an example, I'll help you out.

Answer 3

I have f(x)=a(x+4)^2 (x-1)

Answer 4

What is the (x-1) doing? Is it being multiplied?

Answer 5

Okay so you have a * (x+4)(x+4)(x-1), correct? You want to turn this into one polynomial?

Answer 6

Wait I worded it wrong so I need to take the function f(x)=a(x+4)^2 (x-1) and expand it

Answer 7

That doesn't really help. Can you send a picture of the problem so I can understand? Are you talking about series expansion? Or polynomials?

Answer 8

Given \( f(x) = a(x + 4)^2(x - 1) \):



I think this is it?

1. Expand \( (x + 4)^2 \):
\[
(x + 4)^2 = x^2 + 8x + 16
\]

2. Multiply by \( (x - 1) \):
\[
(x^2 + 8x + 16)(x - 1) = x^3 + 7x^2 + 8x - 16
\]

3. Multiply by \( a \):
\[
f(x) = a(x^3 + 7x^2 + 8x - 16)
\]

Final result:
\[
f(x) = a x^3 + 7a x^2 + 8a x - 16a
\]

Answer 9

Please don't do that again. We aren't even sure that's what he is referring to. Besides, you should not hand people the answer so quickly. If he wanted to know he would do the same AI prompt that you did. It doesn't help people learn; knowledge is gained with understanding.

Answer 10

I know how to write standard for but I’m not too sure about expanding

Answer 11

Ah, do you know how to do FOIL? (First, outside, inside, last)

Essential, (x+4)^2 can be written out as (x+2)(x+2)

First: The first terms in each are multiplied. This means the first term in (x+2) is x, same with the other (x+2). Two x's being multiplied is x^2
Outside: Outside terms are multiplied. First term is x, and the last one is 2, so you have another 2x
x^2 + 2x
Inside: The two inside terms are multiplied. The second and third terms and 2 and x, which multiply to another 2x
Last: The last terms in each (x+2) are the 2's, which are the last thing to multiply, making 4.
x^2 + 2x + 2x + 4 which simplifies to x^2 + 4x + 4

This is the basic idea for foil. multiply each term by every other term, and add the parts together at the end. For example: (a+b+c)(d+e) would look like a*d + a*e + b*d + b*e + c*d + c*e

I'll add a little visual for understanding.

Answer 12

Essentially*

Answer 13

Theres also another method to doing this, called the box method. This is often easier for bigger polynomials. Which will be better if you're multiplying (x^2 + 4x + 4)(x-1), which ill make an example problem thats similar for you

Answer 14

Oh I didn’t know I could do the box method for this

Answer 15

This is an example of polynomial expansion (not your specific problem). You can use the box method as long as you make it fit the amount of terms you have. Since its 3 terms being multiplied by two terms, you can just make it a 2x3 box.

Answer 16

Oh ok that makes sense

Answer 17

wdh