1.1 Integers and Rational Numbers

www.ck12.org Chapter 3. Polynomials and Exponents, Part 1c) The volume of this shape = (area of the base)(height).Areao fthebase = x(x + 2)= x 2 + 2xHeight = 2x + 1Volume = (x 2 + 2x)(2x + 1)= 2x 3 + x 2 + 4x 2 + 2x= 2x 3 + 5x 2 + 2xd) The volume of this shape = (area of the base)(height).Areao fthebase = (4a − 3)(2a + 1)= 8a 2 + 4a − 6a − 3= 8a 2 − 2a − 3Height = a + 4Volume = (8a 2 − 2a − 3)(a + 4)so the volume is 8a 3 + 30a 2 − 11a − 12.Practice SetMultiply the following monomials.1. (2x)(−7x)2. (10x)(3xy)3. (4mn)(0.5nm 2 )4. (−5a 2 b)(−12a 3 b 3 )5. (3xy 2 z 2 )(15x 2 yz 3 )Multiply and simplify.6. 17(8x − 10)7. 2x(4x − 5)8. 9x 3 (3x 2 − 2x + 7)9. 3x(2y 2 + y − 5)10. 10q(3q 2 r + 5r)11. −3a 2 b(9a 2 − 4b 2 )12. (x − 3)(x + 2)13. (a + b)(a − 5)14. (x + 2)(x 2 − 3)15. (a 2 + 2)(3a 2 − 4)16. (7x − 2)(9x − 5)17. (2x − 1)(2x 2 − x + 3)18. (3x + 2)(9x 2 − 6x + 4)19. (a 2 + 2a − 3)(a 2 − 3a + 4)65