Question

5x+15y+25= 2x²y-5xy²= -8mn-12n²= k(m+n)+c(m+n)= m²kc+n²kc=

Answer 1

$5x + 15y + 25 = 5(x + 3y + 5)$

$2 {x}^{2} y - 5x {y}^{2} = xy(2 x- 5y)$

$- 8mn - 12 {n}^{2} = - 4n(2m + 3)$

$k(m + n) + c(m + n) = (m + n)(k + c)$

${m}^{2} kc + {n}^{2} kc = kc( {m}^{2} + {n}^{2} )$

Answer 2

To find the values of variables in the given equations, let's solve each equation step-by-step:

1. 5x + 15y + 25 = 2x²y - 5xy² Rearrange the terms: 2x²y - 5xy² - 5x - 15y - 25 = 0

2. -8mn - 12n² = k(m + n) + c(m + n) Factor out common terms on both sides:

   • (k + c)(m + n) = -8mn - 12n²

3. m²kc + n²kc = 0 Factor out common terms on the left side: kc(m² + n²) = 0

Now, let's analyze each equation one by one:

1. 2x²y - 5xy² - 5x - 15y - 25 = 0

This is a polynomial equation with two variables, x and y. Without additional information or constraints, we can't solve for specific values of x and y. However, we can try to simplify or factor the equation if possible.

2. • (k + c)(m + n) = -8mn - 12n²

This equation involves four variables: k, c, m, and n. Similar to the first equation, without more context or information, we cannot determine specific values for these variables.

3. kc(m² + n²) = 0

Here, we have three variables: k, c, m, and n. For this equation to be true, one of the factors must be equal to zero:

1. kc = 0
2. m² + n² = 0

For the first case, if kc = 0, it means either k or c or both are equal to zero. However, we can't determine the specific values without further information.

For the second case, m² + n² = 0, for this equation to be true, both m and n must be equal to zero. However, we still can't find the values of k and c without additional constraints or equations.

In summary, without more information, the given equations are not sufficient to determine specific values for the variables x, y, k, c, m, and n. If you have any additional constraints or equations related to these variables, please provide them, and I'll be happy to assist further.