It is: 7xy/21yz = x/3z when simplified
4
1xy
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,...
The factors of 7xyz would include 1, 7, x, y, z, and any combination of these factors. Factors are numbers or variables that can be multiplied together to give the original number or expression. In this case, the factors of 7xyz would be all the numbers and variables that divide evenly into 7xyz without leaving a remainder.
4
5
To determine if the expressions (5x - 3xy - 5x) and (7xy - 4y) are equivalent, we can simplify the first expression. Simplifying (5x - 3xy - 5x) results in (-3xy). The second expression, (7xy - 4y), does not simplify to (-3xy). Therefore, the two expressions are not equivalent.
(xy - 7)(x^2y^2 + 7xy + 49)
-9x^2 - 15x
The GCF is 7xy^3
5x(7xy + 6x + 8)
A quadratic. For example, x^2 + 3x - 7xy - 12y - 25 = 0
1xy
-7xy(x4y2 + 6x2y - 5)
No, the expression (7xy - 11) is not a linear equation because it contains the product of two variables, (x) and (y). A linear equation in two variables typically has the form (Ax + By + C = 0), where the variables are not multiplied together. In this case, the presence of the term (xy) indicates that the equation is nonlinear.
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.)