Question

1) Does the order in which the polynomials you add polynomials affect the sum? Does the order in which you subtract polynomials affect the difference? Explain

2)If the parentheses are removed from (3m^2-5m)+(12m^2+7m-10) is the new expression equivalent to the original? If the parentheses are removed from (3m^2-5m)-(12m^2+7m-10) is the new expression equivalent to the original? Explaiin

Answer 1

1) Consider the polynomials f(x) and g(x), their sum is f(x)+g(x) = g(x)+f(x), this shows that the way you add them doesn't effect the result. Difference between them f(x)-g(x)≠g(x)-f(x), showing the order you subtract them matters.
2) Removing braces doesn't effect the first one while the second one has to be simplified if braces are to be removed.

Answer 2

1) The sum of polynomials satisfy the commutative property. Hence, the order in which you add the polynomials does not effect the sum. 

Eg:  2x + 5x = 7x  and 5x + 2x = 7x

But the subtraction of the polynomials doesnt satisfy the commutative property. Hence, the order is very important for subtraction. 

Eg 5x - 2x = 3x   but 2x - 5x = –3x

2) IF the parentheses are removed the given expression the resultant expression is equivalent to the original. After the simplification of the expression, the new expression is also equivalent to the original.