It is: 7xy/21yz = x/3z when simplified
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Assuming that x, y and z are all prime, then they are 1, 7, x, y, z, 7x, 7y, 7z, xy, xz, yz, 7xy, 7xz, 7yz, xyz, 7xyz.
Usually simple substitutions enable such expressions to be seen as quadratic expressions. The substitutions x = a2 and y = b2 give a4 + b4 - 7a2b2 = x2 - 7xy + y2 which does not have any rational factors. Consequently, the quartic in a and b does not have rational factors.
All of these are monomials. The binomials are algebraic expressions consisting of two terms. A term is a constant, a variable, or a combination of constants and variables. 2y, 2x, y, and 2xy consisting of only one term, so they are monomials. Examples of binomials: 2 + 5, 2x + 3, 3x + 7y, 2xyz + 7xy,...
7 + 4x = 34 + x Don't expect answers for homework, but I'll do this one. The rule for ANY math equation is to apply the same operation to both sides including using the same numbers. (operations are +,-,/,*, etc). And you can combine numbers with the same type of variable or lack of (e.g. 2x + 3x = 5x or 2 + 2 = 4 or 5yx + 7xy = 13xy) (7 + 4x) - 7 = (34 + x) -7 // subtract 7 on both sides 4x = 26 + x (4x) - x = (27 + x ) - x // subtract x on both sides 3x = 27 (3x)/3 = 27/3 // divide by 3 on both sides x = 9 check the answer 7 + 4*(9) = 34 + 9 7 + 36 = 43 43 = 43; so correct Writing this is a long form, but do this when you are first learning, then simplify your writing as you figure tricks or can do it in you head.
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(xy - 7)(x^2y^2 + 7xy + 49)
The GCF is 7xy^3
-9x^2 - 15x
5x(7xy + 6x + 8)
A quadratic. For example, x^2 + 3x - 7xy - 12y - 25 = 0
-7xy(x4y2 + 6x2y - 5)
gcf(35x², 7xy², 21x²y²) = 7x 35x² = 5 times 7 times x² 7xy² = 7 times x times y² 21x²y² = 3 times 7 times x² times y² hcf = 7 times x = 7x (I've written the multiplication as times instead of using the × symbol to avoid confusion with the unknown x.)
It means "1" is the magic number, like if you were to have a math problem that looked like this:7xy-xy+3xIt means use the "magic one" to combine 7xy and 1xyIf that doesn't make sense you should probably state the question like this:What does the "Magic 1" mean in math?
(xy + 7)(x^2y^2 - 7xy + 49)
x3y2 + 7x2y3 + 7xy - 2 + x2y3 + 8x3y2 - 3xy - 7 =9x3y2 + 8x2y3 + 4xy - 9 =xy ( 9x2y + 8xy2 + 4) - 9 =xy ( xy(9x + 8y) + 4) - 9 .This is still messy, but it's simpler than the octonomial in the question,and we can't see any more that can be done with it.