Warm-UpWarm-Up

Collect like terms and arrange in descending order.

5 minutes

1) 4x3 + 6x4 – 2x4 + 8x

2) 3x – 5x + 5 + 2x0

3) Evaluate 4x3 + x2 – 2 for x = 0 and x = 1

Addition / Subtraction of Addition / Subtraction of PolynomialsPolynomials

Objectives: •To add polynomials•To subtract polynomials

Example 1Example 1Add

(5x2 + 3x + 4) + (3x2 + 5)

= 8x2

+ 3x

+ 9

Example 2Example 2Add

(7x2y3 + xy) + (1 – 2x2y3)

= 5x2y3

+ xy

+ 1

PracticePractice

1) (3x2 + 2x – 2) + (-2x2 + 5x + 5)

Add.

2) (31x4 + x2 + 2x – 1) + (-7x4 + 5x3 – 2x + 2)3) (4a2b – 5a + 3) + (-2a2b – 2a – 4)

Example 3Example 3Add.

(2x4 – 5x2 + 4x + 5) + (5x4 + 7x3 – 2x2 – 2x)

2x4 + 0x3 – 5x2 + 4x + 55x4 + 7x3 – 2x2 – 2x + 07x4 +

7x3 – 7x2 +

2x+ 5

Example 4Example 4

Add.

(-3x4y3 + 6x3y3 – 6x2 + 5xy5 + 1) + (5x5 – 3x3y3 – 5xy5)

-3x4y3 + 6x3y3 – 6x2 + 5xy5 + 15x5 - 3x3y3 - 5xy5

5x5 – 3x4y3

+ 3x3y3

– 6x2 + 1

PracticePractice

1) (-2m3 – 5m2 – 2m – 4) + (m4 – 6m2 + 7m – 10)

Add.

2) (-3x4y3 – 5xy + 2) + (x4y3 + x2 + 2xy + 5)

Subtraction of Subtraction of PolynomialsPolynomials

Objectives: •To subtract polynomials

Example 1Example 1Subtract.

(5x2 + 3x - 2) - (2x2 + 1)

= 5x2 + 3x - 2

- 2x2 - 1

= 3x2 + 3x - 3

Example 2Example 2Subtract.

(2x2y2 + 3xy3 – 4y4) - (x2y2 – 5xy3 + 3y – 2y4)

= 2x2y2 + 3xy3 – 4y4

- x2y2 + 5xy3 – 3y + 2y4

= x2y2 + 8xy3 – 2y4 – 3y

PracticePractice

1) (5x4 + 4) – (2x2 – 1)

Subtract.

2) (-7m3 + 2m + 4) – (-2m3 – 4)

3) (-3a2b4 + 5ab - 4) - (-4a3 + 11a2b4 – 2a - 6)

Example 3Example 3Subtract.

(8x3 + 6x2 – 3x + 5) – (5x3 – 3x2 + 2x – 4)

8x3 + 6x2 – 3x + 5-5x3 + 3x2 - 2x + 4

3x3 – 9x2 - 5x + 9

Example 4Example 4

Subtract.

(2a4b + 5a3b2 – 4a2b3) – (4a4b + 2a3b2 – 4ab)

2a4b + 5a3b2 – 4a2b3

-4a4b - 2a3b2 + 4ab

-2a4b + 3a3b2 – 4a2b3 + 4ab

PracticePractice

1) (-2m3 – 5m2 – 2m – 4) - (m4 – 6m2 + 7m – 10)

Subtract.

2) (-3x4y3 – 5xy + 2) - (x4y3 + x2 + 2xy + 5)

RULE!RULE!• In order to add or subtract, you must

have ….• The same BASE and the same

EXPOENNT!

Example Example • You can add 3x2 + 2x2 together

• You CAN NOT add 3x3 + 2x2 together!