1. 1-1 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Polynomials in Several Variables Evaluating Polynomials Like Terms and Degree Addition and Subtraction Multiplication 4.7

2. 1-2 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Evaluate the polynomial 5 + 4x + xy 2 + 9x 3 y 2 for x =  2 and y = 3. Solution

3. 1-3 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Sage and Scribe Evaluate the polynomial 5 + 4x + xy 2 + 9x 3 y 2 for x =  1 and y = 2.

4. 1-4 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example The surface area of a right circular cylinder is given by the polynomial 2  rh +  r 2 where h is the height and r is the radius of the base. A barn silo has a height of 50 feet and a radius of 9 feet. Approximate its surface area. Solution

5. 1-5 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Identify the coefficient and the degree of each term and the degree of the polynomial 10x 3 y 2  15xy 3 z 4 + yz + 5y + 3x 2 + 9. TermCoefficientDegreeDegree of the Polynomial 10x 3 y 2  15xy 3 z 4 yz 5y 3x 2 9

6. 1-6 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Sage and Scribe TermCoefficientDegreeDegree of Polynomia l TermCoefficientDegreeDegree of Polynomial

7. 1-7 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Like Terms Like, or similar terms either have exactly the same variables with exactly the same exponents or are constants. For example, in the polynomial 10x 3 y 2  15xy 3 z 4 + 1 + 5y + 3x 3 y 2 + 9. 10x 3 y 2 and ______are like terms and 9 and _______are like terms.

8. 1-8 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Combine like terms to form equivalent expressions. 10x 2 y + 4xy 3  6x 2 y  2xy 3 Solution

9. 1-9 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Sage and Scribe Add: (  6x 3 + 4y  6y 2 ) + (7x 3 + 5x 2 + 8y 2 ) Subtract: (5x 2 y + 2x 3 y 2 + 4x 2 y 3 + 7y)  (5x 2 y  7x 3 y 2 + x 2 y 2  6y)

10. 1-10 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. ♦Example

11. 1-11 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Sage and Scribe Multiply (a)(x + 6y)(2x  3y)

12. 1-12 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Sage and Scribe Multiply (c)(  3x 3 y 2 + 7t)(3x 3 y 2 + 7t) Multiply (d) (3x + 1  4y)(3x + 1 +4y)