Section 2.4 - Adding And Subtracting Polynomials

The given expression is a polynomial expression. To simplify it, we combine like terms. The terms with n^2 are 8n^2 and n^2, which add up to 9n^2. The terms with n are -3n and -2n, which add up to -5n. Therefore, the simplified form of the expression is 9n^2 - 5n.

To simplify the given expression, we need to combine like terms. The terms inside the parentheses can be simplified by distributing the negative sign to both terms inside. This gives us -6x - 2. Now, we can combine like terms by adding the coefficients of the x terms and the constant terms separately. The x terms -4x and -6x can be combined to give us -10x. The constant terms 3 and -2 can be combined to give us 1. Therefore, the simplified expression is -10x + 1. However, none of the given options match this simplified expression. Hence, the correct answer is not provided.

The given expression is 6x^2 + 4y + y^2 - 9y. To simplify this expression, we can combine like terms. The terms 4y and -9y can be combined to give -5y. Therefore, the simplified expression is 6x^2 + y^2 - 5y.

The perimeter of a triangle is calculated by adding the lengths of all three sides. In this case, the lengths of the sides are given as 3m^2 + 7n - 2, -2n^2 + 7m - 4n + 5, and 8m^2 + n^2 + 6m + 1. To find the perimeter, we simply add these three expressions together, which results in 11m^2 - n^2 + 13m + 3n + 4. Therefore, the correct answer is 11m^2 - n^2 + 13m + 3n + 4.

The correct answer is 2x^2 - 5x + 3. To find the missing terms that need to be added to x^2 + 3x - 2, we can compare the coefficients of the like terms in both expressions. The coefficient of x^2 in the given expression is 3, while in x^2 + 3x - 2 it is 1. Therefore, we need to add 2x^2 to the expression. The coefficient of x in the given expression is -2, while in x^2 + 3x - 2 it is 3. Therefore, we need to subtract 5x from the expression. Lastly, the constant term in the given expression is 1, while in x^2 + 3x - 2 it is -2. Therefore, we need to add 3 to the expression. This gives us the expression 2x^2 - 5x + 3.

The given expression is a subtraction of two expressions inside parentheses. To simplify, we need to distribute the negative sign to each term inside the second parentheses. This changes the subtraction to addition and changes the signs of the terms inside the second parentheses. Simplifying further, we combine like terms by adding or subtracting coefficients of the same variables. In this case, the resulting expression is 9x^2 - 5xy + 6y^2.

The given statement is true. When adding or subtracting polynomials, like terms can be simplified by adding or subtracting their numerical coefficients. However, the exponents of like terms should not be added or subtracted, as they represent the degree of the variables in the polynomial. The correct way to simplify a sum or difference of polynomials is by adding or subtracting the coefficients of like terms only.

To find the sum of -3x^2z^2 - 5z^2 and 2x^2z^2 + x^2 - 3z^2, we need to combine like terms. The x^2z^2 terms can be combined to give 2x^2z^2 - 3x^2z^2 = -x^2z^2. The x^2 terms can be combined to give x^2 + x^2 = 2x^2. The z^2 terms can be combined to give -5z^2 - 3z^2 = -8z^2. Therefore, the sum is -x^2z^2 + 2x^2 - 8z^2. The correct answer, 5x^2z^2 + x^2 + 2z^2, is not a valid sum and does not match the given question.

The perimeter of a rectangle is calculated by adding up all the sides. In this case, the length of the rectangle is 2x^2 + 5x + 1 and the width is 3x^2 + 4x + 3. To find the perimeter, we add up the lengths of all four sides. The length of the top and bottom sides is 2x^2 + 5x + 1, and the length of the left and right sides is 3x^2 + 4x + 3. Adding these four sides together gives us 2(2x^2 + 5x + 1) + 2(3x^2 + 4x + 3) = 4x^2 + 10x + 2 + 6x^2 + 8x + 6 = 10x^2 + 18x + 8. Therefore, the correct answer is 10x^2 + 18x + 8.