5.4 SUBTRACTING POLYNOMIALS

VOCABULARY

Word

Know It Well

Have Heard It

or Seen It

No Clue

Subtracting Polynomials (EASY)

(– 4x) – (– 6x)

2. ADD ZERO PAIRS if necessary

1. TAKE AWAY the appropriate number of tiles

• You must SUBTRACT six negative x

– tiles

• BUT, YOU ONLY HAVE 4 NEGATIVE

TILES! HOW CAN YOU TAKE AWAY

6 OF THEM?

• You must ADD two more negative

x-tiles because there are only four

negative x-tiles

• YOU MUST ADD THEM AS A ZERO

PAIR!!

• ADD two negative x-tiles and two

positive x – tiles as 2 zero pairs of

x-tiles 2x

Subtracting Polynomials

(3x² – 4x) – (2x² – 6x)

2. ADD ZERO PAIRS if necessary

1. TAKE AWAY the appropriate number of tiles

• You must SUBTRACT two positive

x2 – tiles and six negative x – tiles

• You must ADD two more negative

x-tiles because there are only four

negative x-tiles

• ADD two negative x-tiles and two

positive x – tiles as 2 zero pairs of

x-tiles

Subtracting Polynomials

(3x² – 4x) – (2x² – 6x)

2. ADD ZERO PAIRS if necessary

• Now, you can take away (SUBTRACT)

two positive x2 – tiles and six

negative x – tiles

• The remaining tiles represent the

ANSWER

x² + 2x

Subtracting Polynomials

(3x² – 4x) – (2x² – 6x)

2. COLLECT and COMBINE like terms

1. REMOVE the BRACKET and subtract each term

• Use the properties of Integers

• MINUS in front of the bracket

means ALL THE SIGNS inside of the

bracket MUST BE CHANGED 3x² – 4x – (+ 2x²– 6x)

3x² – 4x – 2x² + 6x

3x² – 2x² – 4x + 6x

x² + 2x

Example 1

(-2a² + a – 1) – (a² – 3a + 2)

2. ADD ZERO PAIRS if necessary

1. TAKE AWAY the appropriate number of tiles

• You must SUBTRACT one positive a2 – tile,

three negative a – tiles , and two positive 1 -

tiles

• To SUBTRACT a2, ADD a zero pair of a2-tiles.

• To SUBTRACT -3a, ADD 3 zero pairs of a-tiles.

• To SUBTRACT 2, ADD 2 zero pairs of 1-tiles.

Example 1

(-2a² + a – 1) – (a² – 3a + 2) 2. ADD ZERO PAIRS if necessary • You must SUBTRACT one a2 – tile, three -a –

tiles , and two number 1 - tiles

• To SUBTRACT a2, ADD a zero pair of a2-tiles.

• To SUBTRACT -3a, ADD 3 zero pairs of a-tiles.

• To SUBTRACT 2, ADD 2 zero pairs of 1-tiles.

• Remove tiles for (a² – 3a + 2)

-3a² + 4a – 3

(5x² – 3xy + 2y²) – (8x² – 7xy – 4y²)

• Use the properties of Integers

• MINUS in front of the bracket

means ALL THE SIGNS inside of the

bracket MUST BE CHANGED

–3x² + 4xy + 6y²

Example 2

(5x² – 3xy + 2y²) – (8x² – 7xy – 4y²)

5x² – 3xy + 2y² – 8x² + 7xy + 4y²

5x² – 8x² – 3xy + 7xy + 2y² + 4y²

(5x² – 3xy + 2y²) – (+ 8x² – 7xy – 4y²)

5.4 HOMEWORK Page: 235 - 237

Problems: 4, 5 (a,d,h), 8, 10, 13

5.1 - 5.4 REVIEW