ExerciseExerciseFind the opposite (additive inverse) of 4.3.Find the opposite (additive inverse) of 4.3.

– 4.3– 4.3

Find the opposite (additive inverse) of – 27.Find the opposite (additive inverse) of – 27.

2727

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Find the opposite (additive inverse) of x.Find the opposite (additive inverse) of x.

– x– x

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Find the opposite (additive inverse) of 3y.Find the opposite (additive inverse) of 3y.

– 3y– 3y

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Find the opposite (additive inverse) of 7z – 16.Find the opposite (additive inverse) of 7z – 16.

– 7z + 16– 7z + 16

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PolynomialPolynomial Additive InverseAdditive Inverse

3x + 43x + 4 – 3x – 4– 3x – 4

2y – 62y – 6 – 2y + 6– 2y + 6

– x2 + 2x – 5– x2 + 2x – 5 x2 – 2x + 5x2 – 2x + 5

Find the opposite of x2 – 3x + 4.Find the opposite of x2 – 3x + 4.

– (x2 – 3x + 4)– (x2 – 3x + 4) = – x2 + 3x – 4= – x2 + 3x – 4

Example 1Example 1

Find the opposite of 3x – 2.Find the opposite of 3x – 2.

– 3x + 2– 3x + 2

ExampleExample

Find the additive inverse of x3 – 4x + 3.Find the additive inverse of x3 – 4x + 3.

– x3 + 4x – 3– x3 + 4x – 3

ExampleExample

Find the additive inverse of 4xy – 3z2.Find the additive inverse of 4xy – 3z2.

– 4xy + 3z2– 4xy + 3z2

ExampleExample

Subtract 15x – (– 2x – 8y).Subtract 15x – (– 2x – 8y).

15x – (– 2x – 8y)15x – (– 2x – 8y)

= 17x + 8y= 17x + 8y

= 15x + 2x + 8y= 15x + 2x + 8y= (15x + 2x) + 8y= (15x + 2x) + 8y

Example 2Example 2

Subtract (5x – 2y) – (3x + 4y).Subtract (5x – 2y) – (3x + 4y).

(5x – 2y) – (3x + 4y)(5x – 2y) – (3x + 4y)

= 2x – 6y= 2x – 6y

= (5x – 2y) + (– 3x – 4y)= (5x – 2y) + (– 3x – 4y)= (5x – 3x) + (– 2y – 4y)= (5x – 3x) + (– 2y – 4y)

= 2x + (– 6y)= 2x + (– 6y)

Example 3Example 3

Subtract 9x – (2x + 3).Subtract 9x – (2x + 3).

7x – 37x – 3

ExampleExample

Subtract (12x + 5) – (8x + 3).Subtract (12x + 5) – (8x + 3).

4x + 24x + 2

ExampleExample

Subtract (8x2 – 9x – 3) – (2x2 + 6x – 4).Subtract (8x2 – 9x – 3) – (2x2 + 6x – 4).(8x2 – 9x – 3) – (2x2 + 6x – 4)(8x2 – 9x – 3) – (2x2 + 6x – 4)

6x2 – 15x + 16x2 – 15x + 1

(8x2 – 9x – 3) + (– 2x2 – 6x + 4)(8x2 – 9x – 3) + (– 2x2 – 6x + 4)(8x2 – 2x2) + (– 9x – 6x) + (– 3 + 4)(8x2 – 2x2) + (– 9x – 6x) + (– 3 + 4)6x2 + (– 15x) + 16x2 + (– 15x) + 1

Example 4Example 4

Subtract (x3 + 2x2 – 9x + 14) – (7x2 – 6x – 4).Subtract (x3 + 2x2 – 9x + 14) – (7x2 – 6x – 4).(x3 + 2x2 – 9x + 14) + (– 7x2 + 6x + 4)(x3 + 2x2 – 9x + 14) + (– 7x2 + 6x + 4)

x3 – 5x2 – 3x + 18x3 – 5x2 – 3x + 18

x3 + (2x2 – 7x2) + (– 9x + 6x) + (14 + 4)x3 + (2x2 – 7x2) + (– 9x + 6x) + (14 + 4)x3 + (– 5x2) + (– 3x) + 18x3 + (– 5x2) + (– 3x) + 18

Example 5Example 5

Subtract (2x3 – 1) – (6x2 + 8x).Subtract (2x3 – 1) – (6x2 + 8x).

(2x3 – 1) – (6x2 + 8x)(2x3 – 1) – (6x2 + 8x)

2x3 – 6x2 – 8x – 12x3 – 6x2 – 8x – 1(2x3 – 1) + (– 6x2 – 8x)(2x3 – 1) + (– 6x2 – 8x)

Example 6Example 6

Subtract (3a + 2b – 5) – (2a – 2b + 5).Subtract (3a + 2b – 5) – (2a – 2b + 5).

a + 4b – 10a + 4b – 10

ExampleExample

Subtract (x3 + 6x2 – 7x + 4) – (2x3 + x2 + 3x – 8).Subtract (x3 + 6x2 – 7x + 4) – (2x3 + x2 + 3x – 8).

– x3 + 5x2 – 10x + 12– x3 + 5x2 – 10x + 12

ExampleExample

Subtract (8x3 + 5x – 7) – (x4 + 3x3 – x2 + 1).Subtract (8x3 + 5x – 7) – (x4 + 3x3 – x2 + 1).

– x4 + 5x3 + x2 + 5x – 8– x4 + 5x3 + x2 + 5x – 8

ExampleExample

Arrange the polynomials in descending powers of the variable, and then subtract: (3x – 4x2 + 2) – (2x + 5x2 + 3).

Arrange the polynomials in descending powers of the variable, and then subtract: (3x – 4x2 + 2) – (2x + 5x2 + 3).

– 9x2 + x – 1– 9x2 + x – 1

ExampleExample

Subtract: (x5 – 3x2 + 1 + 4x3) – (x4 – 5x + x2 – 2x3).Subtract: (x5 – 3x2 + 1 + 4x3) – (x4 – 5x + x2 – 2x3).

x5 – x4 + 6x3 – 4x2 + 5x + 1x5 – x4 + 6x3 – 4x2 + 5x + 1

ExampleExample

Subtract: (2x – 8x4 + 7x2 – 9x3) – (8x2 – 4x3 – 3x + x4).

Subtract: (2x – 8x4 + 7x2 – 9x3) – (8x2 – 4x3 – 3x + x4).

– 9x4 – 5x3 – x2 + 5x– 9x4 – 5x3 – x2 + 5x

ExerciseExercise

Subtract: (5 – x3 + 8x – 2x2) – (4x2 – 7 + 9x – 5x3).

Subtract: (5 – x3 + 8x – 2x2) – (4x2 – 7 + 9x – 5x3).

4x3 – 6x2 – x + 124x3 – 6x2 – x + 12

ExerciseExercise

Set up the problem vertically and subtract by using the definition of subtraction: (4a + 2b – 7c) – (– 6a + 3b + 9c).

Set up the problem vertically and subtract by using the definition of subtraction: (4a + 2b – 7c) – (– 6a + 3b + 9c).

10a – b – 16c10a – b – 16c

ExerciseExercise

Set up the problem vertically and subtract by using the definition of subtraction: (6x2 – 9x + 4) – (– 3x2 – 12x – 5).

Set up the problem vertically and subtract by using the definition of subtraction: (6x2 – 9x + 4) – (– 3x2 – 12x – 5).

9x2 + 3x + 99x2 + 3x + 9

ExerciseExercise