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1. Multiplying Monomials Chapter 8.1

2. Multiplying Monomials • Lesson Objective: NCSCOS 1.01 – Write the equivalent forms of algebraic expressions to solve problems • Students will know how to apply the laws of exponents when multiplying monomials.

3. Multiplying Monomials • Example 1- • Simplify: x2 * x3 • Remember: x2 = x * x which can also be written as xx • x2 = x * x and x3 = x * x * x • Therefore x2 * x3 = (x*x)*(x*x*x) = xx * xxx = xxxxx • There are 5 x’s in the answer • Therefore x2 * x3 = x5 • Rule: When multiplying monomials you must add the exponents together. Xm * xn = xm+n

4. Multiplying Monomials • 33 * 34 • x3 * x4 • x5(x3) • x7(x-2) Now you try!

5. Multiplying Monomials • 33 * 34 • x3 * x4 • x5(x3) • x7(x-2) Now you try! 37 x7 x8 x5

6. Multiplying Monomials • Example 2- • Simplify (2x3)(3x4) • Multiply the numbers together first: 2 * 3 = 6 • Multiply the variables together second: x3 * x4 = x7 • Put the numbers and letters back together for your answer: 6x7 • Rule: When multiplying monomials you multiply the numbers and letter separately

7. Multiplying Monomials • 3x3 * 4x2 • 5x4(2x3) • -2x2(4x) • -7x(-3x3) Your Turn!

8. Multiplying Monomials • 3x3 * 4x2 • 5x4(2x3) • -2x2(4x) • -7x(-3x3) Your Turn! 12x5 10x7 -8x3 21x4

9. Multiplying Monomials • Example 3- • Simplify (-2x2y3)(3x5y2) • Multiply the numbers together first: –2 * 3 = -6 • Multiply the x’s separately: x2 * x5 = x7 • Multiply the y’s separately: y3 * y2 = y5

10. Multiplying Monomials (-2x2y3)(3x5y2) -6 x7 y5

11. Multiplying Monomials • 3x3y2 * 4x2y2 • 5x4y3(2x3y4) • -2x2y2(4xy) • -7xy(-3x3y3) More for you 12x5y4 10x7y7 -8x3y3 21x4y4

12. Multiplying Monomials • Example 4 • Simplify (x3)2 • Remember, (x3)2 = (x3) * (x3) = xxx * xxx • Therefore (x3)2 = x6 • Rule: When a monomial with an exponent is then raised to an exponent you multiply the exponents together. (Xm)n = xm*n • You can always write out x3 twice and add the exponents

13. Multiplying Monomials • (x2)3 • (x4)4 • (x3)7 Practice Makes Perfect!

14. Multiplying Monomials • (x2)3 • (x4)4 • (x3)7 Practice Makes Perfect! x6 x16 x21

15. Multiplying Monomials • Example 5 • Simplify: 2x2(3x3)2 • Remember order of operations, exponents come before multiplication! • Also, any number squared means to multiply it by itself • Therefore: 2x2(3x3)(3x3) • Multiply the numbers: 2 * 3 * 3 = 18 • Multiply the variables: x2 * x3 * x3 = x8 • Put the numbers and letters back together: 18x8 Combination Problems

16. Multiplying Monomials • 2x2(3x3)2 • (4x3)2(2x5) • (3x4)3(2x3)2 One more try

17. Multiplying Monomials • 2x2(3x3)2 • (4x3)2(2x5) • (3x4)3(2x3)2 One more try 18x8 32x11 108x18

18. Multiplying Monomials • x2 * x3 • 3x(2x3) • -2x3(4x4) • (x4)3 • 2x3(3x4)2 Quiz 8.1

19. Multiplying Monomials • x2 * x3 • 3x(2x3) • -2x3(4x4) • (x4)3 • 2x3(3x4)2 Quiz 8.1 x5 6x4 -8x7 x12 18x11