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Simplify the expression.
1. (–3x3)(5x)
ANSWER
–15x4
2. 9x – 18x
ANSWER
–9x
3. 10y2 + 7y – 8y2 – 1
ANSWER
2y2 + 7y – 1
Check your HW 5.2
Add & Subtract Polynomials
Monomial: 1 term
x
2
Binomial: 2 terms
x  3x
Trinomial: 3 terms
x 2  3x  2
These are all
polynomials
2
Adding Polynomials: Combine the like terms
Like Terms – Terms that have the same variables with the same exponents on
them
Combining Like Terms: Add the coefficients of each all like terms
Ex.
3x + (-5x) = [3 + (-5)]x
= -2x
Example:
Rewrite
Add :
4 x 2  8 x  9 and -x 2  3x  6
(4 x 2  8x  9)  (-x 2  3x  6)
4 x 2  x 2  8 x  3x  9  6
Combine
Like Terms
3x 2  11x  3
EXAMPLE 1
2. Add 3y3 – 2y2 – 7y and –4y2 + 2y – 5
(3y3 – 2y2 – 7y) + (–4y2 + 2y – 5)
3y3 – 2y2 – 4y2 – 7y + 2y – 5
3y3
–
6y2
– 5y – 5
Gather like terms
Combine like terms
EXAMPLE 2
4. Subtract 4z2 + 9z – 12 from 5z2 – z + 3
from
(5z2 – z + 3) – (4z2 + 9z – 12
Remember to
distribute the –
5z2 – z + 3 – 4z2 – 9z + 12
through the ( )
5z2 – 4z2 – z – 9z + 3 + 12
z2 – 10z + 15
Gather like terms
Combine like terms
GUIDED PRACTICE
for Examples 1 and 2
Find the sum
5. (t2 – 6t + 2) + (5t2 – t – 8)
t2 + 5t2 – 6t – t + 2 – 8
6t2 – 7t – 6
GUIDED PRACTICE
for Examples 1 and 2
Find the difference
6. (8d – 3 + 9d3) – (d3 – 13d2 – 4)
8d – 3 + 9d3 – d3 + 13d2 + 4
9d3 – d3 + 13d2 + 8d – 3 + 4
8d3 + 13d2 + 8d + 1
There are three techniques you can
use for multiplying polynomials.
It’s all about how you write it…
1) Distributive Property-arrow multiplication
2) FOIL – also arrow multiplication!
3) Box Method
I use arrow multiplication most often, you may
use the method you like best.
Remember, FOIL reminds you to
multiply the:
First terms
Outer terms
Inner terms
Last terms
The FOIL method is ONLY used when
you multiply 2 binomials. It is an
acronym and tells you which terms to
multiply.
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
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
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!
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
Multiply 2 binomials
Combine like terms
Multiply the third
binomial
Combine like terms
Follow the pattern
Simplify
Classwork
Finish 5.3
Homework Assignment
Textbook
Page 352 Quiz 1- 16