Okay, I'm working with ultiplying Polynomials, and I just can't figure this one out! Here it is:
(h+k)(h squared-2hk+3k squared)
haha, I don't know how to make an exponent on the computer :-), but anyway, please help me figure it out!
powers are usually written this way...
(h+k)(h^2 - 2hk + 3k^2)
which becomes
h^3 -2h^2k + 3hk^2 + kh^2 - 2hk^2 + 3k^3
= h^3 - h^2k + hk^2 + 3k^3
oh, I tried to solve it and got 3hk^2+h^3 I'm guessing that's wrong?
I solved it like this: h^3-2hk^2+3hk^2+1hk^2-2hk^2+3hk^2=3hk^2+h^3
for the terms inside
-2h^2k + h^2k = -h^2k
and
3hk^2 - 2hk^2 = hk^2
look at my expansion and compare it to yours,
a term in hk^2 is not the same as a h^2k term.
No problem! I can help you with that. To multiply polynomials, you can use the distributive property, which states that for any numbers or variables a, b, and c, (a + b) * c = a * c + b * c.
In your case, you want to multiply (h + k) by (h^2 - 2hk + 3k^2). So, you can distribute the terms of (h + k) to each term inside the parentheses.
First, let's distribute h:
h * (h^2 - 2hk + 3k^2) = h * h^2 - h * 2hk + h * 3k^2
This simplifies to:
h^3 - 2h^2k + 3hk^2
Next, let's distribute k:
k * (h^2 - 2hk + 3k^2) = k * h^2 - k * 2hk + k * 3k^2
This simplifies to:
kh^2 - 2h^2k + 3k^3
Now, combine the two results:
(h + k)(h^2 - 2hk + 3k^2) = h^3 - 2h^2k + 3hk^2 + kh^2 - 2h^2k + 3k^3
Now, you can simplify further by combining like terms. In the expression above, notice that we have two terms with h^2k:
-2h^2k + kh^2
They can be combined to give:
(h + k)(h^2 - 2hk + 3k^2) = h^3 + kh^2 - 2h^2k - 2h^2k + 3hk^2 + 3k^3
Finally, simplifying this further, we get:
(h + k)(h^2 - 2hk + 3k^2) = h^3 + kh^2 - 4h^2k + 3hk^2 + 3k^3
And there you have it! The product of (h + k) and (h^2 - 2hk + 3k^2) is h^3 + kh^2 - 4h^2k + 3hk^2 + 3k^3.