5.3 Adding Polynomials

Adding Polynomials with Algebra Tiles We can use algebra tiles to model an addition sentence. (3s2 + 2s – 6) + (-s2 – 2s + 1) Combine the tiles and group the matching tiles.

Remove the zero pairs. The remaining tiles are: They represent 2s2 - 5

Adding polynomials Symbolically Add: (3c2 + 5c – 6) + (2c2 – 3c + 4) Remove the brackets. = 3c2 + 5c – 6 + 2c2 – 3c + 4 Group like terms. = 3c2 + 2c2 + 5c – 3c – 6 +4 Add the coefficients of like terms. = 5c2 + 2c - 2

Determining a polynomial for the perimeter of a rectangle Write a polynomial for the perimeter of the rectangle. The perimeter is the sum of all 4 sides. (2x + 1) + (2x + 1) + (3x + 2) + (3x + 2) = 10x + 6 2x + 1 3x + 2

Adding polynomials in 2 variables (2a2 + a – 3b – 7ab + 3b2) + (-4b2 + 3ab + 6b – 5a + 5a2) = 2a2 + a – 3b – 7ab + 3b2 - 4b2 + 3ab + 6b – 5a + 5a2 = 2a2 + 5a2 + a – 5a – 3b + 6b – 7ab + 3ab + 3b2 - 4b2 = 7a2 - 4a + 3b – 4ab – b2 = 7a2– b2 – 4ab - 4a + 3b

Adding Polynomials Vertically (3m2 + m – 14) + (2m + 9) 3m2 + 1m – 14 2m + 9 3m2 + 3m – 5 Remove the brackets. Align the like terms vertically. The term “m” has no visible coefficient so make it 1. Add the coefficients of the like terms.

Assignment: Pg. 228-230 3, 4, 8 odd,9 odd, 10 all, 17 all