please help me with math?

Question

64X^2(Y-8)+80X(Y-8)+25(Y-8)=
8X^2^N+18X^N+9=

FACTORING

Answer 1

In the first equation you should immediately notice that the term (Y-8) appears in several places. That is a good sign that it can be factored out: (Y-8)*(64x^2+80X+25) The next thing you should notice is that in the term with X, 64 and 25 are squares of 8 and 5, respectively. So you should try and see if that term is the square of a binomial according to the equation (a+b)^2 = a^2 +2ab+b^2. So you would try a binomial of (8X+5), and sure enough 2*8x*5=80x, so the second term is (8x+5)^2. The factors are then (Y-8), (8X+5),(8X+5). Edit: could also be (Y-8), -(8x+5), -(8x+5).

The second one is more difficult. First don't be confused by x^2N. Let Y=X^N, then the equation becomes more familiar quadratic:

8Y^2+18Y+9

You do this by trial and error: you need four numbers. The product of one pair should be 8, the other should be 9. There are only a few possibilities. 8 = 1x8 or 2x4; 9 = 1x9 or 3x3. Therefore the coefficient of Y in the factors is either (y+...)(8y+....) or (2Y+...)(4Y+...) similarly the constant 9 part is either (...+1)(....+9) or (...+3)(...+3). You try this in various combinations until the middle term comes out right. As you can find out, the result is
(4Y+3)(2Y+3). Put back x^N for Y and get the factors (2X^N+3) and (4X^N+3)

Answer 2

put Y-8=K and take out the k,and the expression will be
k(64X^2+80X+25)
now the sum of the roots is 80 and the product is 64*25=1600
64X^2+80X+25=64X^2+40X+40X+25=8X(8X+5)+5(8X+5)
=.(8X+5)^2
so the answer ell be (Y-8)(8X+5)^2

here the sum is 18 and the product is 72.so the middleterm can be split as follows
8X^2N+18XN+9=8X^2N+8XN+9XN+9=8X(XN+1)+9(XN+1)
=>(XN+1)(8X+9)

Answer 3

Please check your question. Some thing wrong