Example 3. Like terms in polynomials can be added or subtracted. Cannot be so added or subtracted. See…

Question

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

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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 4x⁵ and 9x⁵ are like terms because they both have the variable part x⁵. Step 2: Add the coefficients of the like terms. 4x⁵ + 9x⁵ = (4+9)x⁵ = 13x⁵ 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. (7x³ + 5x² − 8x) + (11x³ − 9x² − 2x) = 7x³ + 5x² − 8x + 11x³ − 9x² − 2x Step 2: Combine the coefficients of the like terms. Group x³ terms: 7x³ + 11x³ = (7+11)x³ = 18x³; Group x² terms: 5x² − 9x² = (5−9)x² = −4x²; Group x terms: −8x − 2x = (−8−2)x = −10x Step 3: Write the simplified polynomial. 18x³ − 4x² − 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. All examples are correct.

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

Answer

Step-by-step solution

Part a· 2 steps

Identify like terms.

Add the coefficients of the like terms.

Part b· 2 steps

Identify like terms.

Subtract the coefficients of the like terms.

Part c· 3 steps

Remove the parentheses and group like terms.

Combine the coefficients of the like terms.

Write the simplified polynomial.

Part d· 3 steps
$\text{All examples are correct.}$

Remove the parentheses and group like terms.

Combine the coefficients of the like terms.

Write the simplified polynomial.

Try one yourself

Still stuck on this one?

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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

Answer

Step-by-step solution

Part a· 2 steps

Identify like terms.

Add the coefficients of the like terms.

Part b· 2 steps

Identify like terms.

Subtract the coefficients of the like terms.

Part c· 3 steps

Remove the parentheses and group like terms.

Combine the coefficients of the like terms.

Write the simplified polynomial.

Part d· 3 stepsAll examples are correct.\text{All examples are correct.}All examples are correct.

Remove the parentheses and group like terms.

Combine the coefficients of the like terms.

Write the simplified polynomial.

Try one yourself

Still stuck on this one?

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Part d· 3 steps
$\text{All examples are correct.}$