Question

Find an expression which represents the difference when (6x-3y) is subtracted from (9x+2y) in simplest terms.

Answer 1

The simplest expression which represents the difference when (6x-3y) is subtracted from (9x+2y) is 3x + 5y. Change the sign of each term being subtracted and combine like terms to find the result.

Step-by-step explanation:

To find the expression which represents the difference when (6x-3y) is subtracted from (9x+2y), you need to perform the subtraction operation. Subtraction of polynomials is similar to subtracting numbers, you change the sign of each term in the polynomial being subtracted and then combine like terms. Here is the step-by-step process:

Write down the polynomials: (9x + 2y) - (6x - 3y).

Change the sign of each term in the second polynomial: (9x + 2y) - 6x + 3y.

Combine like terms by adding the coefficients of like terms: (9x - 6x) + (2y + 3y).

Simplify the expression: 3x + 5y.

The simplest form of the expression representing the difference is 3x + 5y.

Answer 2

`3x+5y`

Step-by-step explanation:

Subtract (6x-3y) from (9x+2y):

`(9x+2y)-(6x-3y)`

This can also be seen as:

`(9x+2y)-1(6x-3y)`

Distribute the -1 to (6x-3y):

`(9x+2y)-1(6x)-1(-3y)\\\\(9x+2y)-6x+3y`

Simplify the parentheses:

`9x+2y-6x+3y`

Group like terms:

`(9x-6x)+(2y+3y)`

Combine:

`3x+5y`

This expression can't be further simplified. Therefore, 3x+5y is the answer.

:Done