Download 7-5 Multiply Polynomial by Monomial

7-5 Multiply a Polynomial by a
Monomial
Algebra 1
Glencoe McGraw-Hill
Linda Stamper
You can use the distributive property to multiply a
monomial by a polynomial.
The problem.
x(x2 + 2x + 4)
Distribute.
x(x2) + x(2x)+ x(4) optional step
Simplify.
x3 + 2x2 + 4x
Simplify.
Example 1
Example 2
3m(2m2 + 4m + 6)
4y(y2 – 3y + 5)
Example 3
Example 4
2a2(2a3 – 3a2 + 3)
Example 5
3xy4xy  5y 
3x2(8x2 – 5x + 2)
Example 6

 5a3b 2b  5ab  b2  a2
Don’t forget to write your answer in standard form –
alphabetical descending order.

Simplify.
Example 1
Example 2
3m(2m2 + 4m + 6)
3m(2m2) + 3m(4m) + 3m(6)
6m3 + 12m2 + 18m
4y(y2 – 3y + 5)
4y(y2 + -3y + 5)
4y(y2) + 4y(-3y) + 4y(5)
4 y 3 + - 12y2 + 20y
Undo
double
signs!
4y3  12y2  20 y
Simplify.
Example 3
2a2(2a3 – 3a2 + 3)
2a2(2a3 + -3a2 + 3)
2a2(2a3) + 2a2(-3a2) + 2a2(3)
4 a 5 + - 6a 4 + 6a2
4a5  6a 4  6a2
Undo
double
signs!
Example 4
3x2(8x2 – 5x + 2)
3x2(8x2 + -5x + 2)
3x2(8x2)+ 3x2(-5x) + 3x2(2)
24x 4 + - 15x3 + 6x2
24x4  15x3  6x2
Undo
double
signs!
Example 5
3xy4xy  5y 
3xy4xy   3xy5y 
12x2 y2  15xy
2
Example 6


 5a3b2b   5a3b5ab    5a3b b2    5a3ba3 
 5a3b 2b  5ab  b2  a3
 10 a3b2  25a 4b2  5a3b3  5a6b
 5a6b  25a 4b2  5a3b3  10 a3b2
Simplify.
 

Change subtraction
43d2  5d   dd2   7d  12
to addition.
2
2
Distribute. 43d   45d   dd    d 7d   d12
12d2  20d   d3   7d2   12d
Simplify.
The problem.

4 3d2  5d  d d2  7d  12
 d3  19d2  8d
Simplify.

 

Example 7
 2 4x2  5x  x x2  6x
Example 8
3 2x2  4x  15  6x5x  2


Simplify.
Example 7

 

 24x2  5x     x x2  6x 
 24x2    25x     x x2     x 6x 
 2 4x2  5x  x x2  6x
 8x2  10x  x3  6x2
 x3  14x2  10x
Simplify.


32x2   4x   15   6x5x  2
32x2  3 4x   3 15   6x 5x   6x 2
Example 8
3 2x2  4x  15  6x5x  2
6x2  12x  45  30x2  12x
36x2  45
Solve.
The problem.
yy  12  yy  2  25  2yy  5  15
Distribute.
y2  12y  y2  2y  25  2y2  10 y  15
Combine like
terms.
Use inverse
operations to solve.
2y2  10 y  25  2y2  10 y  15
 2y2
 2y2
 10 y  25  10 y  15
 10 y
 10 y
 25  20y  15
 15
 15
40  20y
2y
Solve.
Example 9
b12  b  7  2b  b 4  b
Example 10
4n  2  5n  63  n   19
Example 11
34w  2  6w  4   3  4w  7 w  2  53w  6
Solve.
Example 9
b12  b  7  2b  b 4  b
12b  b2  7  2b   4b  b2
12b  b2  7  2b  b2
 b2
 b2
12b  7  2b
 2b
 2b
14b  7  0
7 7
14b  7
14 14
1
b
2
Solve.
Example 10
4n  2  5n  63  n   19
4n  8  5n  18  6n  19
9n  8  6n  37
 6n
 6n
15n  8  37
8 8
15n  45
15
15
n 3
Example 11
34w  2  6w  4   3  4w  7 w  2  53w  7 
12w  6  6w  24  3  4w  7w  14  15w  35
18w  15  12w  21
 12w
 12w
6w  15  21
 15  15
6w  6
w 1
7-A6 Pages 392-393 #16-21,26-31,36-39,44.