Adding and Subtracting, Polynomials

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Presentation transcript:

Adding and Subtracting, Polynomials August 10, 2016

Essential question How do I add or subtract polynomials?

Outline Vocabulary Review Like Terms Adding Polynomials Subtracting Polynomials

Vocabulary review Monomial expression Binomial expression Expression with one term 5x 7y2 Binomial expression Expression with 2 terms 4xy + 9z 12ab + 14cd Polynomial expression Expression with more than 2 terms 8x3 + 12x2 – 4x + 6 12x2 + 14x -16

Like Terms Like Terms Unlike Terms 2x, 45x, x, -26x, -x 17x, 17z 15, -2, 27, 9043, 0.6 15y, 19y2, 31y5 3y2, y2, -y2, 26y2 19x, 14xy

Adding Polynomials Add the following polynomials: (9y - 7x + 15a) + (-3y + 8x - 8a) Step 1: Group all like terms together (9y-3y) +(-7x+8x) +(15a-8a) 6y + x +7a Step 2: Make sure the expression is standard form (i.e. decreasing degree order if the same variable is used) Doesn’t apply in above example

Adding Polynomials Add the following polynomials: (3a2 + 3ab - b2) + (4ab + 6b2) Step 1: Group all like terms together 3a2 + (3ab + 4ab) + (- b2 + 6b2) 3a2 + 7ab + 5b2 Step 2: Make sure the expression is standard form (i.e. decreasing degree order if the same variable is used) Doesn’t apply in above example

Adding Polynomials x2 + 3x + 7y + xy + 8 x2 + 4y + 2x + 3 3x + 7y + 8 1 1 Y 1 1 1 Y 1 1 1 Y x2 + 3x + 7y + xy + 8 x2 + 4y + 2x + 3 3x + 7y + 8 x2 + 11xy + 8

Adding Polynomials (Alternate Method) Add the following polynomials using column form: (4x2 – 2xy + 3y2) + (-3x2 –xy + 2y2) (4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2) Line up your like terms 4x2 - 2xy + 3y2 + -3x2 - xy + 2y2 X2 -3xy + 5y2

Subtracting Polynomials Subtract the following polynomials: (9y - 7x + 15a) - (-3y + 8x - 8a) Step 1: Rewrite subtraction as adding the opposite. (9y - 7x + 15a) + (+ 3y - 8x + 8a) Step 2: Group the like terms. (9y + 3y)+ (- 7x - 8x) + (15a + 8a) 12y-15x+23a

Subtracting Polynomials Subtract the following polynomials: (7a - 10b) - (3a + 4b) Step 1: Rewrite subtraction as adding the opposite. (7a – 10b) + (- 3a – 4b) Step 2: Group the like terms. (7a - 3a)+ (- 10b – 4b) 4a -14b

subtracting Polynomials (Alternate Method) Add the following polynomials using column form: (4x2 – 2xy + 3y2) - (-6x2 +5xy - 7y2) (4x2 - 2xy + 3y2) + (6x2 - 5xy + 7y2) Line up your like terms 4x2 - 2xy + 3y2 + 6x2 - 5xy + 7y2 10X2 -7xy + 10y2

Examples Find the sum or difference. (5a – 3b) + (2a + 6b) 3a – 9b

Examples Find the sum or difference. (5a – 3b) – (2a + 6b) 3a – 9b