ADDING& SUBTRACTINGPOLYNOMIALS

JOURNAL ENTRY ERROR ANALYSIS

A student simplified 6a³ -a³ and got a 6 as a result. Write an explanation of the student’s error using the words coefficient and like terms.

Collect like terms and Arrange each polynomial in descending order for x

3x²y³ + - 2xy + 3x³y² - 5x²y³ - 8xy + 4x³y²

Collect like terms and Arrange each polynomial in descending order for b

4a3 + 7a2b + b3 - 3ab2 + b3 - a3 + 3a2b

Add PolynomialsColumn form

Add 3x3+2x2-x-7 and x3-10x2+8. 3x3 + 2x2 – x – 7

+ x3 – 10x2 + 8 Line up like terms

4x3 – 8x2 – x + 1

YOU TRY

Add 7x3+6x2+ 4x + 1 and -7x3+ 6x2+ - 4x + 8.

7x3 + 6x2 +4x +1 + -7x3 + 6x2 +-4x + 8 Line up like

terms 12x2 + 9

12x2 + 9

HORIZONTAL FORMAT : COMBINE LIKE TERMS

(8x3 – 3x2 – 2x + 9) +(-2x3 - 6x2 +x - 1)= (8x3 – 2x3)+(-3x2 – 6x2)+(-2x + x) + (9 – 1)= 6x3 + -9x2 + -x + 8 = 6x3 – 9x2 – x + 8

YOUR TURN

(7x3 – 4x2 – 4x + 3) +(- 2x2 -3x3 +3x - 5)= (7x3 – 3x3)+(-4x2 – 2x2)+(-4x + 3x) + (3 – 5)= 4x3 + -6x2 + x + -2

= 4x3 – 6x2 + x + -2

Add the polynomials

(-3cd³ + 6d² + 2cd – 1) + (-3d² + 2cd +1)

(9x -7x +2x² + 5) + (8x + 4x - 2x) + (2x² - 8)

(4x²y – 5xy + 7) + (8x²y + 7xy² + 3xy – 2)

(7y - 6y + 3y³ - 1) + (6y - 3y³ + 6y² + 5)

Subtracting Polynomials

To perform subtraction we add the additive inverse.

2 – 1 = 2 + -1, a – b = a + -b What is the additive inverse of 4x² + 2x – 1 -(4x² + 2x – 1)= -1(4x² + 2x – 1) - 4x² - 2x + 1

Find the additive inverse of

2x² - 4

5x + 3x³ - 4y + 3

Subtract Polynomials Column form

(4x3y2+3x2-x-7) – (x3y2-10x2+8) (4x3y2+3x2-x-7) +(-x3y2+10x2-8) 4x3y2 + 3x2 – x – 7

+ - x3y2 + 10x2 - 8 Line up like terms

3x3y2 + 13x2 – x - 15

YOUR TURN

(8x3y2 + 2x2 - 3x-4) – (9x3y2 - 5x2 - 8) (8x3y2 + 2x2 – 3x -4) +(-9x3y2 + 5x2 +8) 8x3y2 + 2x2 – 3x – 4 - 9x3y2 + 5x2 + 8 Line up like

terms -x3y2 + 7x2 – 3x + 4

HORIZONTAL FORMAT : COMBINE LIKE TERMS

(8x3 – 3x2 – 2x + 9) - (-2x3 - 6x2 + x - 1)= (8x3 – 3x2 – 2x + 9) + (2x3 + 6x2 - x +1) (8x3+ 2x3)+(-3x2 + 6x2)+(-2x + -x) + (9 + 1)= 10x3 + 3x2 + -3x + 10 = 10x3 +3x2 + -3x + 10

Your turn Horizontal format

(5x² + 2) – (3x² - 8)

(2x – 5) – (-6x + 5)

Subtract Polynomials

(-2cd³ + 5d² + 2cd – 1) - (-3d² + 2cd +1)

(5x -7x +3x² + 5) - (6x - 4x - 2x)

(7x²y – 4xy + 7) - (3x²y + 7xy² - 3xy – 2) +(2xy + 3)

(8y - 6y + 2y³ - 1) - (5y + 2y³ + 6y² + 5)

EXAMPLES: ADDING

(9x3 – 2x + 1) + (5x2 + 12x -4) = 9x3 + 5x2 – 2x + 12x + 1 – 4 = 9x3 + 5x2 + 10x – 3

(2x2 + 3x) - (-3x2 - x + 4)= 2x2 + 3x + 3x2 + x + -4 = 2x2 + 3x2 + 3x + x + -4 = 5x2 + 4x + -4