i need some help really bad with some binomial theorem and others?

Question

1. using the binomial theorem expand (x+4y)^4

2. find the equation of a circle having a radius of 10 and a center (4,-7)

3. identify the center and radius of the circle represented by x^2+10x+y^2-8y=19

Answer 1

x^4 + 16x^3y + 96 x^2 y^2 + 256 x y^3 + 256 y^4

(x-4)^2 + (y+7)^2 = 10

(-5, 4), radius 60


-----------------------------
edit, don't use firefly's method for question 1.
imagine you had a higher power than 4. what if it was to the power of 10? would you want to square something that big? just remember the binomial formula. its quite easy.
(a+b)^c = (c choose i) * a^(c-i) * b^i
where i is the i'th term in the expansion.

Answer 2

2

Answer 3

1. First, square it to get (x+4y)^2 = x^2 + 8xy + 16y^2
Then, square (x^2+8xy+16y^2) =
(x^2 + 8xy + 16y^2)(x^2+8xy+16y^2)
To do this, you just multiply every term in the first part by ever term in the second part. To get you started...
x^2*x^2 + x^2*8xy + x^2*16y^2 + 8xy*(the whole second part) + 16y^2*(the whole second part)...

2. a circle formula is (x-centerx)^2 + (y-ycenter)^2 = radius^2
so all you need to do is plug in the numbers (being careful of + and - signs).

3) For this, you need to complete the squares. For example (x+5)^2 = x^2 + 10x + 25
And (y-4)^x = y^2 - 8y + 16.
Now you just have to make the constant parts come out right!

Answer 4

The Binomial Theorem is: ( x + y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4. So on your particular question, everywhere you spot an x, you plug in 2a. everywhere you spot a y, you plug in b^2. so that you get (2A + B^2)^4 = (2A)^4 + 4(2A)^3(B^2) + 6(2A)^2(B^2)^2 + 4(2A)(B^2)^3 + (B^2)^4 So, (2A +B^2)^4 = 16A^4 + 32A^3B^2 + 24A^2B^4 + 8AB^6 + B^8 <== it rather is your answer :) The Binomial theorem strengthen isn't some thing mysterious in spite of the undeniable fact that... it rather is fairly in hardship-free words a time-saver. The formula is mutually with the similar subject that you'll get in case you likely did (2A + B^2)(2A + B^2)(2A +B^2)(2A + B^2). So in case you want to double study your answer, you're waiting to do it that way too. you'll see in spite of the undeniable fact that that there are diverse words and also you may favor to combine words after each and every and each and every step. You do it plenty quicker by technique of skill of making use of the Binomial Theorem.