Example 3. Like terms in polynomials can be added or subtracted. Cannot be so added or subtracted. See Problems 1.2 and 1.3. a) 4x5 + 9x5 = 13x5 b) 12xy - 3xy = 9xy c) (7x3 + 5x2 - 8x) + (11x3 - 9x2 - 2x) = 18x3 - 4x2 - 10x d) (24x - 17y) + (6x + 5z) = 30x - 17y + 5z

This example demonstrates how to add and subtract like terms in polynomials. Let's verify each part.

a) Step 1: Identify like terms. The terms $4x^5$ and $9x^5$ are like terms because they both have the variable part $x^5$. Step 2: Add the coefficients of the like terms. $4x^5 + 9x^5 = (4+9)x^5 = 13x^5$ The example is correct.

b) Step 1: Identify like terms. The terms $12xy$ and $3xy$ are like terms because they both have the variable part $xy$. Step 2: Subtract the coefficients of the like terms. $12xy - 3xy = (12-3)xy = 9xy$ The example is correct.

c) Step 1: Remove the parentheses and group like terms. $(7x^3 + 5x^2 - 8x) + (11x^3 - 9x^2 - 2x) = 7x^3 + 5x^2 - 8x + 11x^3 - 9x^2 - 2x$ Step 2: Combine the coefficients of the like terms. Group $x^3$ terms: $7x^3 + 11x^3 = (7+11)x^3 = 18x^3$ Group $x^2$ terms: $5x^2 - 9x^2 = (5-9)x^2 = -4x^2$ Group $x$ terms: $-8x - 2x = (-8-2)x = -10x$ Step 3: Write the simplified polynomial. $18x^3 - 4x^2 - 10x$ The example is correct.

d) Step 1: Remove the parentheses and group like terms. $(24x - 17y) + (6x + 5z) = 24x - 17y + 6x + 5z$ Step 2: Combine the coefficients of the like terms. Group $x$ terms: $24x + 6x = (24+6)x = 30x$ The term $-17y$ has no other like terms. The term $5z$ has no other like terms. Step 3: Write the simplified polynomial. $30x - 17y + 5z$ The example is correct.

All the given examples correctly demonstrate the addition and subtraction of like terms in polynomials. $\boxed{All examples are correct.}$

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