I. Model Problems. II. Practice III. Challenge Problems VI. Answer Key
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I. Model Problems. II. Practice III. Challenge Problems VI. Answer Key
Web Resources
Monomials www.mathwarehouse.com/algebra/polynomial/monomials/how-to-multiplymonomials.php Polynomials http://www.mathwarehouse.com/algebra/polynomial/
www.mathwarehouse.com/algebra/polynomial/how-to-multiply-polynomials.php © www.MathWorksheetsGo.com All Rights Reserved Commercial Use Prohibited Terms of Use: By downloading this file you are agreeing to the Terms of Use Described at http://www.mathworksheetsgo.com/downloads/terms-of-use.php .
Online Graphing Calculator(free): www.mathworksheetsgo.com/calculator/
I. Model Problems A monomial is an expression that is a number, variable or product of a number and variables. Examples of monomials: –3, 4x, 5xy, y2 To multiply monomials, multiply all the coefficients and all the variables. Example 1 Simplify 2x3(7x5). = 14x3x5
Multiply the coefficients.
= 14x8
Multiply variables.
The answer is 14x8. To divide monomials, divide the coefficients and the variables. 20x 7 y 6 Example 2 Simplify . 4x 2 y 5 Divide the coefficients. 5x 7 y 6 = 3 5 x y = 5x4y Divide variables. The answer is 5x4y. When you have power of a power, everything inside the parentheses gets raised to the power. You multiply exponents. Example 3 Simplify (5x2y4)3. = 53x2•3y4•3
Raise everything to the 3rd power.
= 125x6y12
Simplify.
The answer is 125x6y12.
To multiply rational expressions with monomials, in the numerator and the denominator, follow the rules of simplifying monomials. 15x 7 y 6 xy 6 Example 4 Multiply . 2x 2 y 5 5y 3 Multiply the numerators and the 15x 7 y 6 xy 6 = 2 5 denominators. 2x y 5y 3
15x 7 y 6 xy 6 = 10x 2 y 5 y 3
Multiply the coefficients.
15x 8 y12 = 10x 2 y 8
Multiply the variables (add exponents).
3x 8 y12 = 2x 2 y 8 3 = x6 y4 2
Simplify coefficients. Divide variables (subtract exponents).
3 6 4 x y . 2 (3x 2 y 3 )3 4x 2 y 5 Example 5 Multiply . 2x 2 y 5 18y 3 Simplify power to a power. 27x 6 y 9 4x 2 y 5 = 2x 2 y 5 18y 3 Multiply the coefficients and 108x 8 y14 = variables. 36x 2 y 8
The answer is
3x 8 y14 = 2 8 x y = 3x 6 y 6 The answer is 3x6y6.
Simplify coefficients. Divide variables (subtract exponents).
II. Practice Simplify. 1. 4x5(9x3)
2. –9x5(7x7)
3. –7x5(3x2)
4. 20x4(3x9)
5. 8x7y5(10x2y)
6. –4x9 y15(3x9y5)
20x14 7. 10x 3
30x13 8. 15x 8
120x10 9. 10x 5
45y16 10. 9 y8
65x19 y17 11. 13x 5 y 5
30x 27 y 39 12. 5x10 y 8
13. (4x2y5)3
14. (2x3y2)5
15. (–2x3y7)3
16. (7x2yz4)2
17. (10x24y20)2
18. (–3x5y10)3
3x 6 y11 20x 5 y 8 19. 10x 2 y 5 12x 4 y 3
24x12 y 23 15x 3 y 3 20. 4x 7 y 20 25x 2 y 2
24x19 y 20 15x12 y19 21. 12x17 y14 3x 9 y15
14x 8 y 6 (2x 3 y 3 )2 22. 7x 3 y 3 2x 2 y
III. Challenge Problems 23. What is the area of a rectangle with length 6xy7 inches and width (5x2y) inches? Write your answer as an expression in terms of x and y.
20x19 y 20 4x54 y19 z 20 (4x12 y19 z)3 24. Simplify . 8x17 y14 (2x 9 y15 )3 3x 4 y15 z 2
25. Correct the Error There is an error in the student work shown below: Question: (3x4y9)5 . Solution:
= (3x4y9)5 = 15x20y45
What is the error? Explain how to solve the problem. _________________________________________________________ _________________________________________________________
IV. Answer Key 1. 36x8 2. -63x12 3. -21x7 4. 60x13 5. 80x9y6 6. -12x18y20 7. 2x11 8. 2x5 9. 12x5 10. 5y8 11. 5x14y12 12. -6x17y31 13. 64x6y15 14. 32x15y10 15. -8x9y21 16. 49x4y2z8 17. 100x48y40 18. -27x15y30 19. (1/2)x6y11 20. (18/5)x6y4 21. 10x5y10 22. 4x9y8 23. 30x2y8 in2 24. (80/3)x61y22z21 25. The student multiplied the coefficient by the exponent instead of raising the coefficient to the power. The correct answer is 243x20y45.
I. Model Problems. II. Practice III. Challenge Problems VI. Answer Key
Web Resources
Monomials www.mathwarehouse.com/algebra/polynomial/monomials/how-to-multiplymonomials.php Polynomials http://www.mathwarehouse.com/algebra/polynomial/
www.mathwarehouse.com/algebra/polynomial/how-to-multiply-polynomials.php © www.MathWorksheetsGo.com All Rights Reserved Commercial Use Prohibited Terms of Use: By downloading this file you are agreeing to the Terms of Use Described at http://www.mathworksheetsgo.com/downloads/terms-of-use.php .
Online Graphing Calculator(free): www.mathworksheetsgo.com/calculator/
I. Model Problems A monomial is an expression that is a number, variable or product of a number and variables. Examples of monomials: –3, 4x, 5xy, y2 To multiply monomials, multiply all the coefficients and all the variables. Example 1 Simplify 2x3(7x5). = 14x3x5
Multiply the coefficients.
= 14x8
Multiply variables.
The answer is 14x8. To divide monomials, divide the coefficients and the variables. 20x 7 y 6 Example 2 Simplify . 4x 2 y 5 Divide the coefficients. 5x 7 y 6 = 3 5 x y = 5x4y Divide variables. The answer is 5x4y. When you have power of a power, everything inside the parentheses gets raised to the power. You multiply exponents. Example 3 Simplify (5x2y4)3. = 53x2•3y4•3
Raise everything to the 3rd power.
= 125x6y12
Simplify.
The answer is 125x6y12.
To multiply rational expressions with monomials, in the numerator and the denominator, follow the rules of simplifying monomials. 15x 7 y 6 xy 6 Example 4 Multiply . 2x 2 y 5 5y 3 Multiply the numerators and the 15x 7 y 6 xy 6 = 2 5 denominators. 2x y 5y 3
15x 7 y 6 xy 6 = 10x 2 y 5 y 3
Multiply the coefficients.
15x 8 y12 = 10x 2 y 8
Multiply the variables (add exponents).
3x 8 y12 = 2x 2 y 8 3 = x6 y4 2
Simplify coefficients. Divide variables (subtract exponents).
3 6 4 x y . 2 (3x 2 y 3 )3 4x 2 y 5 Example 5 Multiply . 2x 2 y 5 18y 3 Simplify power to a power. 27x 6 y 9 4x 2 y 5 = 2x 2 y 5 18y 3 Multiply the coefficients and 108x 8 y14 = variables. 36x 2 y 8
The answer is
3x 8 y14 = 2 8 x y = 3x 6 y 6 The answer is 3x6y6.
Simplify coefficients. Divide variables (subtract exponents).
II. Practice Simplify. 1. 4x5(9x3)
2. –9x5(7x7)
3. –7x5(3x2)
4. 20x4(3x9)
5. 8x7y5(10x2y)
6. –4x9 y15(3x9y5)
20x14 7. 10x 3
30x13 8. 15x 8
120x10 9. 10x 5
45y16 10. 9 y8
65x19 y17 11. 13x 5 y 5
30x 27 y 39 12. 5x10 y 8
13. (4x2y5)3
14. (2x3y2)5
15. (–2x3y7)3
16. (7x2yz4)2
17. (10x24y20)2
18. (–3x5y10)3
3x 6 y11 20x 5 y 8 19. 10x 2 y 5 12x 4 y 3
24x12 y 23 15x 3 y 3 20. 4x 7 y 20 25x 2 y 2
24x19 y 20 15x12 y19 21. 12x17 y14 3x 9 y15
14x 8 y 6 (2x 3 y 3 )2 22. 7x 3 y 3 2x 2 y
III. Challenge Problems 23. What is the area of a rectangle with length 6xy7 inches and width (5x2y) inches? Write your answer as an expression in terms of x and y.
20x19 y 20 4x54 y19 z 20 (4x12 y19 z)3 24. Simplify . 8x17 y14 (2x 9 y15 )3 3x 4 y15 z 2
25. Correct the Error There is an error in the student work shown below: Question: (3x4y9)5 . Solution:
= (3x4y9)5 = 15x20y45
What is the error? Explain how to solve the problem. _________________________________________________________ _________________________________________________________
IV. Answer Key 1. 36x8 2. -63x12 3. -21x7 4. 60x13 5. 80x9y6 6. -12x18y20 7. 2x11 8. 2x5 9. 12x5 10. 5y8 11. 5x14y12 12. -6x17y31 13. 64x6y15 14. 32x15y10 15. -8x9y21 16. 49x4y2z8 17. 100x48y40 18. -27x15y30 19. (1/2)x6y11 20. (18/5)x6y4 21. 10x5y10 22. 4x9y8 23. 30x2y8 in2 24. (80/3)x61y22z21 25. The student multiplied the coefficient by the exponent instead of raising the coefficient to the power. The correct answer is 243x20y45.
