Maths Qs :|?

Question

plz help me

a) factorize
(x+y)^4 - (x-y)^4

b) what is the remainder when 5x^3 + 3x^2 + 6x+7 is devided by (2x-1)

thaaaaaaaaaanks

Answer 1

a)

(x + y)^4 - (x - y)^4

You have to factor this as a difference of squares. Remember that a^2 - b^2 factors as (a - b) (a + b). These are actually two squares, because a^4 is the same as (a^2)^2. As a result, this factors into

[(x + y)^2 - (x - y)^2] [(x + y)^2 + (x - y)^2]

{Note: *always* be careful with the bracketing!}

Notice that in the first set of brackets, we have a difference of squares yet again. This leads to some more factorization.

[(x + y) - (x - y)] [(x + y) + (x - y)] [(x + y)^2 + (x - y)^2]

Now, we can actually simplify the stuff in the first two sets of brackets.

[x + y - x + y] [x + y + x - y] [(x + y)^2 + (x - y)^2]

[2y] [2x] [(x + y)^2 + (x - y)^2]

[4xy] [(x + y)^2 + (x - y)^2]

Answer 2

a) factorize
(x+y)^4 - (x-y)^4
= [(x+y)^2- (x-y)^2][(x+y)^2 + (x-y)^2]
=[(x+y)^2- (x-y)(x+y)][(x+y)^2 + (x-y)(x+y)]

b) what is the remainder when 5x^3 + 3x^2 + 6x+7 is devided by (2x-1)
Just do synthetic diision and you should get 11.375

Answer 3

a) this is the difference of two squares... a²-b² = (a+b)(a-b)
[(x+y)²+(x-y)²][(x+y)²-(x-y)²]
You should know the squares by now
[x²+2xy+y²+x²-2xy+y²] mulitplied by [x²+2xy+y²-x²+2xy-y²]
[2x²+2y²][4xy]
8(x²+y²)(xy)

b) I hate doing long division of polynomials. The first term is 5/2 x². You're on your own after that.