Please check.

(-6m^2n+3mn^2-5mn+2)+(4m^2n+2mn^2-6mn-9)
Answer: -2m^2n+5mn^2-11mn-7

(2x^4-3x^2+7x)-(5x^3+2x^2-3x+5)
Answer: 2x^4-5x^3-5x^2+10x-5

(a-8)(a-1)
Answer: a^2-9a+8

(z+6)^2
Answer: z^2+12z+36

(5x+2y)^2
Answer: 25x^2+20xy+4y^2
Is that order okay? Does it matter?

(2x-7)(2x+7)
Answer: 4x^2-49

Yes, your answers look correct! The order is okay. The polynomial is usually arranged so that the exponent of one variable is in increasing or decreasing order.

The order of the terms in an expression does not matter when it comes to addition or subtraction. Both orders (-6m^2n+3mn^2-5mn+2) + (4m^2n+2mn^2-6mn-9) and (4m^2n+2mn^2-6mn-9) + (-6m^2n+3mn^2-5mn+2) would yield the same answer.

That being said, let's go step by step to find the answer to the first expression:

(-6m^2n+3mn^2-5mn+2) + (4m^2n+2mn^2-6mn-9)

Combine like terms:

(-6m^2n + 4m^2n) + (3mn^2 + 2mn^2) + (-5mn - 6mn) + (2 - 9)

Simplify each set of like terms:

-2m^2n + 5mn^2 - 11mn - 7

So the final answer to the first expression is: -2m^2n + 5mn^2 - 11mn - 7.

Let's move to the second expression:

(2x^4-3x^2+7x) - (5x^3+2x^2-3x+5)

To perform the subtraction, distribute the negative sign to each term inside the parentheses:

2x^4 - 3x^2 + 7x - 5x^3 - 2x^2 + 3x - 5

Reorder the terms:

2x^4 - 5x^3 - 5x^2 + 10x - 5

So the final answer to the second expression is: 2x^4 - 5x^3 - 5x^2 + 10x - 5.

Moving on to the third expression:

(a-8)(a-1)

To multiply these binomials, you can use the distributive property:

(a * a) + (a * -1) + (-8 * a) + (-8 * -1)

Simplify each term:

a^2 - a - 8a + 8

Combine like terms:

a^2 - 9a + 8

So the final answer to the third expression is: a^2 - 9a + 8.

Now, let's tackle the fourth expression:

(z+6)^2

To square a binomial, you can use the formula: (a + b)^2 = a^2 + 2ab + b^2

In this case, a = z and b = 6:

(z + 6)^2 = z^2 + 2(z)(6) + 6^2

Simplify each term:

z^2 + 12z + 36

So the final answer to the fourth expression is: z^2 + 12z + 36.

Lastly, the fifth expression:

(5x+2y)^2

Using the same binomial formula, a = 5x and b = 2y:

(5x + 2y)^2 = (5x)^2 + 2(5x)(2y) + (2y)^2

Simplify each term:

25x^2 + 20xy + 4y^2

So the final answer to the fifth expression is: 25x^2 + 20xy + 4y^2.

Regarding your question about the order of terms, as I mentioned earlier, the order does not matter when it comes to addition or subtraction. However, when multiplying or dividing terms, the order can affect the result. In the case of (2x-7)(2x+7), the order does not matter because it is a simple multiplication of two binomials. Regardless of the order, you will end up with the same result: 4x^2 - 49.