The document discusses multiplying polynomials by monomials. It explains that to multiply a polynomial by a monomial, each term inside the polynomial parentheses should be multiplied by the monomial. This will preserve the number of terms. Examples are provided to demonstrate distributing the monomial to each term and then multiplying the terms. Readers are instructed to work through practice problems in their notebook and check their work.

1. Multiplying
Polynomials
Module 9 - Topic 2
Part 1

2. Multiply a Polynomial by a
Monomial
Multiply each term
inside the parenthesis
2
( 2
3x 2x − 7x + 5 )
by the monomial
outside the
parenthesis.
The number of terms
inside the parenthesis
will be the same as
after multiplying.

3. Multiply a Polynomial by a
Monomial
Multiply each term
inside the parenthesis
2
(
3x 2x − 7x + 52
)
by the monomial
outside the
3x 2
( 2x ) + 3x ( −7x ) + 3x ( 5 )
2 2 2
parenthesis.
The number of terms
inside the parenthesis
will be the same as
after multiplying.

4. Multiply a Polynomial by a
Monomial
Multiply each term
inside the parenthesis
2
(
3x 2x − 7x + 52
)
by the monomial
outside the
3x 2
( 2x ) + 3x ( −7x ) + 3x ( 5 )
2 2 2
parenthesis.
The number of terms
inside the parenthesis
will be the same as
after multiplying.

5. Multiply a Polynomial by a
Monomial
Multiply each term
inside the parenthesis
2
(
3x 2x − 7x + 52
)
by the monomial
outside the
3x 2
( 2x ) + 3x ( −7x ) + 3x ( 5 )
2 2 2
parenthesis.
The number of terms
inside the parenthesis
2
(
3x 2x − 7x + 5 2
)
will be the same as
after multiplying.

6. Multiply a Polynomial by a
Monomial
Multiply each term
inside the parenthesis
2
(
3x 2x − 7x + 52
)
by the monomial
outside the
3x 2
( 2x ) + 3x ( −7x ) + 3x ( 5 )
2 2 2
parenthesis.
The number of terms
inside the parenthesis
2
(
3x 2x − 7x + 5 2
)
will be the same as 4
6x − 21x + 15x 3 2
after multiplying.

7. Multiply a Polynomial by a
Monomial
Review this Cool Math site to learn about
multiplying a polynomial by a monomial.
Do the Try It and Your Turn problems in
your notebook and check your answers on
the next slides.

8. Try It - Page 1
Multiply: 4
(
6x 2x + 32
)

9. Try It - Page 1
Multiply: 4
(
6x 2x + 32
)
Distribute the monomial.

10. Try It - Page 1
Multiply: 4
(
6x 2x + 3 2
)
Distribute the monomial.
4 2 4
6x ⋅ 2x + 6x ⋅ 3

11. Try It - Page 1
Multiply: 4
(
6x 2x + 3 2
)
Distribute the monomial.
4 2 4
6x ⋅ 2x + 6x ⋅ 3
Multiply each term.

12. Try It - Page 1
Multiply: 4
(
6x 2x + 3 2
)
Distribute the monomial.
4 2 4
6x ⋅ 2x + 6x ⋅ 3
Multiply each term.
6 4
12x + 18x

13. Try It - Page 1
Multiply: 4
(
6x 2x + 3 2
)
Distribute the monomial.
4 2 4
6x ⋅ 2x + 6x ⋅ 3
Multiply each term.
6 4
12x + 18x
Verify your answer has same number of terms
as inside original ( ). Both have 2 terms.

14. Your Turn - Page 2
multiply:

15. Your Turn - Page 2
multiply:
3
( 5 2
10x 2x + 1 − 3x + x )

16. Your Turn - Page 2
multiply:
3
( 5 2
10x 2x + 1 − 3x + x )
Distribute the monomial.

17. Your Turn - Page 2
multiply:
3
(
10x 2x + 1 − 3x + x5 2
)
Distribute the monomial.
( )
10x 2x + 10x (1) + 10x −3x + 10x ( x )
3 5 3 3
( 2
) 3

18. Your Turn - Page 2
multiply:
3
(
10x 2x + 1 − 3x + x5 2
)
( )
10x 2x + 10x (1) + 10x −3x + 10x ( x )
3 5 3 3
( 2
) 3
Multiply each term.

19. Your Turn - Page 2
multiply:
3
(
10x 2x + 1 − 3x + x 5 2
)
( )
10x 2x + 10x (1) + 10x −3x + 10x ( x )
3 5 3 3
( 2
) 3
Multiply each term. 8 3 5 4
20x + 10x − 30x + 10x

20. Your Turn - Page 2
multiply:
3
(
10x 2x + 1 − 3x + x 5 2
)
( )
10x 2x + 10x (1) + 10x −3x + 10x ( x )
3 5 3 3
( 2
) 3
8 3 5 4
Put in descending 20x + 10x − 30x + 10x
order and verify
number of terms.
(Both have 4 terms.)

21. Your Turn - Page 2
multiply:
3
(
10x 2x + 1 − 3x + x 5 2
)
( )
10x 2x + 10x (1) + 10x −3x + 10x ( x )
3 5 3 3
( 2
) 3
8 3 5 4
Put in descending 20x + 10x − 30x + 10x
order and verify
number of terms. 8 5 4 3
(Both have 4 terms.)
20x − 30x + 10x + 10x

22. Try It - Page 2
Multiply:
2 5
( 2 2 4
4x w w − x + 6xw − 1 + 3x w 8
)

23. Try It - Page 2
Multiply:
2 5
( 2 2 4
4x w w − x + 6xw − 1 + 3x w 8
)
Distribute the monomial.

24. Try It - Page 2
Multiply:
2 5
(
4x w w − x + 6xw − 1 + 3x w 2 2 4 8
)
Distribute the monomial.
5
( 2
) 2 5
( 2
)
4x w ( w ) + 4x w −x + 4x w 6xw + 4x w ( −1) + 4x w 3x w
2 5 2 2 5 2 5
( 4 8
)

25. Try It - Page 2
Multiply:
2 5
(
4x w w − x + 6xw − 1 + 3x w 2 2 4 8
)
5
( 2
) 2 5
( 2
)
4x w ( w ) + 4x w −x + 4x w 6xw + 4x w ( −1) + 4x w 3x w
2 5 2 2 5 2 5
( 4 8
)
Multiply each term.

26. Try It - Page 2
Multiply:
2 5
(
4x w w − x + 6xw − 1 + 3x w 2 2 4 8
)
5
( 2
)
4x w ( w ) + 4x w −x + 4x w 6xw + 4x w ( −1) + 4x w 3x w
2 5 2 2 5
( 2
) 2 5 2 5
( 4 8
)
Multiply each term.
2 6 4 5 3 7 2 5 6 13
4x w − 4x w + 24x w − 4x w + 12x w
Verify answer has 5 terms like original parenthesis.

27. Try this one...
Multiply: ( 2
3x 2x − 5x + 7 )

28. Try this one...
Multiply: ( 2
3x 2x − 5x + 7 )
Distribute the monomial.

29. Try this one...
Multiply: ( 2
3x 2x − 5x + 7 )
Distribute the monomial.
( )
3x 2x + 3x ⋅ ( −5x ) + 3x ( 7 )
2

30. Try this one...
Multiply: ( 2
3x 2x − 5x + 7 )
( )
3x 2x + 3x ⋅ ( −5x ) + 3x ( 7 )
2
Multiply each term.

31. Try this one...
Multiply: ( 2
3x 2x − 5x + 7 )
( )
3x 2x + 3x ⋅ ( −5x ) + 3x ( 7 )
2
Multiply each term.
3 2
6x − 15x + 21x

32. Try this one...
Multiply: 2 2
( 3
−2a b a + 3a b − 4b2 3 5
)

33. Try this one...
Multiply: 2 2
( 3
−2a b a + 3a b − 4b 2 3 5
)
Distribute the monomial.

34. Try this one...
Multiply: 2 2
( 3
−2a b a + 3a b − 4b 2 3 5
)
Distribute the monomial.
( −2a b )( a ) + ( −2a b )( 3a b ) + ( −2a b )( −4b )
2 2 3 2 2 2 3 2 2 5

35. Try this one...
Multiply: 2 2
( 3
−2a b a + 3a b − 4b 2 3 5
)
( −2a b )( a ) + ( −2a b )( 3a b ) + ( −2a b )( −4b )
2 2 3 2 2 2 3 2 2 5
Multiply each term.

36. Try this one...
Multiply: 2 2
( 3
−2a b a + 3a b − 4b 2 3 5
)
( −2a b )( a ) + ( −2a b )( 3a b ) + ( −2a b )( −4b )
2 2 3 2 2 2 3 2 2 5
Multiply each term.
5 2 4 5 2 7
−2a b − 6a b + 8a b

37. Great job working
all those problems!
Proceed to Part 2.