Transcript Multiplying a Monomial and Polynomials

Adding/Subtracting
Polynomials
1. Add the following polynomials:
(9y - 7x + 15a) + (-3y + 8x - 8a)
Group your like terms.
9y - 3y - 7x + 8x + 15a - 8a
6y + x + 7a
2. Add the following polynomials:
(3a2 + 3ab - b2) + (4ab + 6b2)
Combine your like terms.
2
3a
2
b
+ 3ab + 4ab - +
3a2 + 7ab + 5b2
2
6b
3. Add the following polynomials
using column form:
2
2
2
2
(4x - 2xy + 3y ) + (-3x - xy + 2y )
Line up your like terms.
4x2 - 2xy + 3y2
+ -3x2 - xy + 2y2
_________________________
x2 - 3xy + 5y2
4. Subtract the following polynomials:
(9y - 7x + 15a) - (-3y + 8x - 8a)
Rewrite subtraction as adding the
opposite.
(9y - 7x + 15a) + (+ 3y - 8x + 8a)
Group the like terms.
9y + 3y - 7x - 8x + 15a + 8a
12y - 15x + 23a
Multiplying a Monomial
and a Polynomial
Review: When multiplying variables,
add the exponents!
1) Simplify: 5(7n - 2)
Use the distributive property.
5 • 7n - 5 • 2
35n - 10
2)
3
Simplify: a(8a  12)
4
3
3
a 8a  a 12
4
4
6a2 + 9a
3) Simplify: 6rs(r2s - 3)
6rs • r2s - 6rs • 3
6r3s2 - 18rs
4) Simplify: 4t2(3t2 + 2t - 5)
12t4 + 8t3 - 20t2
5) Simplify: - 4m3(-3m - 6n + 4p)
12m4 + 24m3n - 16m3p
6) Simplify:
x
3
(27x2 - 6x + 12)
16x3 - 28x2 + 4x
Fooled ya, didn’t I?!? Ha! Ha!
Here’s the real answer!
-9x3 + 2x2 - 4x
Multiplying Polynomials
There are three techniques you can
use for multiplying polynomials.
The best part about it is that they are all the
same! Huh? Whaddaya mean?
It’s all about how you write it…Here they are!
1)Distributive Property
2)FOIL
3)Box Method
Sit back, relax (but make sure to write this
down), and I’ll show ya!
1) Multiply. (2x + 3)(5x + 8)
Using the distributive property, multiply
2x(5x + 8) + 3(5x + 8).
10x2 + 16x + 15x + 24
Combine like terms.
10x2 + 31x + 24
A shortcut of the distributive property is
called the FOIL method.
The FOIL method is ONLY used when
you multiply 2 binomials. It is an
acronym and tells you which terms to
multiply.
2) Use the FOIL method to multiply the
following binomials:
(y + 3)(y + 7).
(y + 3)(y + 7).
F tells you to multiply the FIRST
terms of each binomial.
y2
(y + 3)(y + 7).
O tells you to multiply the OUTER
terms of each binomial.
y2 + 7y
(y + 3)(y + 7).
I tells you to multiply the INNER
terms of each binomial.
y2 + 7y + 3y
(y + 3)(y + 7).
L tells you to multiply the LAST
terms of each binomial.
y2 + 7y + 3y + 21
Combine like terms.
y2 + 10y + 21
The third method is the Box Method.
This method works for every problem!
Here’s how you do it.
Multiply (3x – 5)(5x + 2)
Draw a box. Write a
polynomial on the top and
side of a box. It does not
matter which goes where.
This will be modeled in the
next problem along with
FOIL.
3x
5x
+2
-5
3) Multiply (3x - 5)(5x + 2)
First terms: 15x2
Outer terms: +6x
Inner terms: -25x
Last terms: -10
Combine like terms.
15x2 - 19x – 10
3x
5x
-5
15x2 -25x
+2 +6x
-10
You have 3 techniques. Pick the one you like the best!
5) Multiply (2x - 5)(x2 - 5x + 4)
You cannot use FOIL because they are
not BOTH binomials. You must use the
distributive property.
2x(x2 - 5x + 4) - 5(x2 - 5x + 4)
2x3 - 10x2 + 8x - 5x2 + 25x - 20
Group and combine like terms.
2x3 - 10x2 - 5x2 + 8x + 25x - 20
2x3 - 15x2 + 33x - 20
5) Multiply (2x - 5)(x2 - 5x + 4)
You cannot use FOIL because they are not BOTH
binomials. You must use the distributive property or
box method.
x2
-5x
+4
2x
2x3
-10x2
+8x
-5
-5x2 +25x
-20
Almost
done!
Go to
the next
slide!
5) Multiply (2x - 5)(x2 - 5x + 4)
Combine like terms!
x2
-5x
+4
2x
2x3
-10x2
+8x
-5
-5x2 +25x
-20
2x3 – 15x2 + 33x - 20
Multiply (2p + 1)(p2 – 3p + 4)
1.
2.
3.
4.
2p3 + 2p3 + p + 4
y2 – y – 12
y2 + 7y – 12
y2 – 7y – 12