6th Grade Math Textbook, Fundamentals

Lesson 14-6 for exercise sets. &KDSWHU 

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Multiply. Write the product in standard form.

1.7(4 y) 2. 11 a(a^2 a) 3. 2 c(c1) 4. 10 m^2 (3m4)

5.w^2 (4 w^10 ) 6.j(64 j^3 ) 7. 10 n( 3 n^2 ) 8. 3 g(g^2  2 g1)

9.Discuss and Write If you substitute 2 for the variable in exercise 1 and

then simplify, what is the value of the given expression? Now substitute

2 for the variable in your answer to exercise 1. Does your answer have

the same value? Use this method to verify the answer you found

for exercise 2.

Multiply:  6 b^2 (4  5 b)

 6 b^2 (4  5 b) ( 6 b^2 )(4) ( 6 b^2 )(5b) Apply the Distributive Property

of Multiplication over Subtraction.

(6 • 4)b^2 (6 • 5)(b^2 • b)

 24 b^2 (30) • b^2 ^1 Apply Law of Exponents for Multiplication.

 24 b^2  30 b^3 Simplify.

Using the Associative and Commutative

Properties, group coefficients and variables.

1

Write a simplified expression for the

area of the rectangle.

Aw Recall the area formula for a rectangle.

(6a^2 a80)a

(6a^2 )a(a)a(80)a Apply the Distributive Property

of Multiplication over Addition.

 6 a^2 ^1 a^1 ^1  80 a Apply the Law of Exponents for Multiplication.

 6 a^3 a^2  80 a Write in standard form.

Substitute the given

dimensions into the formula.

2

The chart below shows some examples of multiplying a

polynomial by a monomial.

a

6 a^2  a  80

Expression Apply the Distributive Property Simplify

10(3y5) 10 • 3y 10 • 5 30 y 50

y(3y5) y• 3yy• 5 3 y^2  5 y

y^2 (3y5) y^2 • 3y y^2 • 5 3 y^3  5 y^2

10 y^2 (3y5) 10 y^2 • 3y 10 y^2 • 5 30 y^3  50 y^2

10 y( 3 y5) 10 y( 3 y)  10 y• 5  30 y^2  50 y