Adding And Subtracting Polynomials

ADDING& SUBTRACTING POLYNOMIALS

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 4a 3 + 7a 2 b + b 3 - 3ab 2 + b 3 - a 3 + 3a 2 b

Add Polynomials Column form Add 3x 3 +2x 2 -x-7 and x 3 -10x 2 +8. 3x 3 + 2x 2 – x – 7 + x 3 – 10x 2 + 8 Line up like terms 4x 3 – 8x 2 – x + 1

YOU TRY Add 7x 3 +6x 2 + 4x + 1 and -7x 3 + 6x 2 + - 4x + 8. 7x 3 + 6x 2 +4x +1 + -7x 3 + 6x 2 +-4x + 8 Line up like terms 12x 2 + 9 12x 2 + 9

HORIZONTAL FORMAT : COMBINE LIKE TERMS (8x 3 – 3x 2 – 2x + 9) +(-2x 3 - 6x 2 +x - 1)= (8x 3 – 2x 3 )+(-3x 2 – 6x 2 )+(-2x + x) + (9 – 1)= 6x 3 + -9x 2 + -x + 8 = 6x 3 – 9x 2 – x + 8

YOUR TURN (7x 3 – 4x 2 – 4x + 3) +(- 2x 2 -3x 3 +3x - 5)= (7x 3 – 3x 3 )+(-4x 2 – 2x 2 )+(-4x + 3x) + (3 – 5)= 4x 3 + -6x 2 + x + -2 = 4x 3 – 6x 2 + 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 (4x 3 y 2 +3x 2 -x-7) – (x 3 y 2 -10x 2 +8) (4x 3 y 2 +3x 2 -x-7) +(-x 3 y 2 +10x 2 -8) 4x 3 y 2 + 3x 2 – x – 7 + - x 3 y 2 + 10x 2 - 8 Line up like terms 3x 3 y 2 + 13x 2 – x - 15

YOUR TURN (8x 3 y 2 + 2x 2 - 3x-4) – (9x 3 y 2 - 5x 2 - 8) (8x 3 y 2 + 2x 2 – 3x -4) +(-9x 3 y 2 + 5x 2 +8) 8x 3 y 2 + 2x 2 – 3x – 4 - 9x 3 y 2 + 5x 2 + 8 Line up like terms -x 3 y 2 + 7x 2 – 3x + 4

HORIZONTAL FORMAT : COMBINE LIKE TERMS (8x 3 – 3x 2 – 2x + 9) - (-2x 3 - 6x 2 + x - 1)= (8x 3 – 3x 2 – 2x + 9) + (2x 3 + 6x 2 - x +1) (8x 3 + 2x 3 )+(-3x 2 + 6x 2 )+(-2x + -x) + (9 + 1)= 10x 3 + 3x 2 + -3x + 10 = 10x 3 +3x 2 + -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 (9x 3 – 2x + 1) + (5x 2 + 12x -4) = 9x 3 + 5x 2 – 2x + 12x + 1 – 4 = 9x 3 + 5x 2 + 10x – 3 (2x 2 + 3x) - (-3x 2 - x + 4)= 2x 2 + 3x + 3x 2 + x + -4 = 2x 2 + 3x 2 + 3x + x + -4 = 5x 2 + 4x + -4

Adding And Subtracting Polynomials

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