Simplify the expression. 1.(–3x 3 )(5x) ANSWER –15x 4 ANSWER –9x–9x 2. 9x – 18x 3. 10y 2 +...
-
Upload
bruce-solomon-booth -
Category
Documents
-
view
225 -
download
2
Transcript of Simplify the expression. 1.(–3x 3 )(5x) ANSWER –15x 4 ANSWER –9x–9x 2. 9x – 18x 3. 10y 2 +...
Simplify the expression.
1. (–3x3)(5x)
ANSWER –15x4
ANSWER –9x
2. 9x – 18x
3. 10y2 + 7y – 8y2 – 1
ANSWER 2y2 + 7y – 1
Monomial: 1 term
2x
Binomial: 2 terms xx 32
Trinomial: 3 terms 232 xx
These are all polynomials
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
Add & Subtract PolynomialsAdd & Subtract Polynomials
Example:63 and 984 :Add 22 x-xxx
Rewrite )63()98(4 22 x-xxx
Combine Like Terms
23x x11 3
69384 22 xxxx
EXAMPLE 1
(3y3 – 2y2 – 7y) + (–4y2 + 2y – 5)
3y3 – 2y2 – 4y2 – 7y + 2y – 5
3y3 – 6y2 – 5y – 5
2. Add 3y3 – 2y2 – 7y and –4y2 + 2y – 5
Gather like terms
Combine like terms
EXAMPLE 2
(5z2 – z + 3) – (4z2 + 9z – 12
5z2 – 4z2 – z – 9z + 3 + 12
z2 – 10z + 15
4. Subtract 4z2 + 9z – 12 from from
5z2 – z + 3 – 4z2 – 9z + 12
Remember to distribute the – through the ( )
Gather like terms
Combine like terms
5z2 – z + 3
GUIDED PRACTICE for Examples 1 and 2
Find the sum
5. (t2 – 6t + 2) + (5t2 – t – 8)
6t2 – 7t – 6
t2 + 5t2 – 6t – t + 2 – 8
GUIDED PRACTICE for Examples 1 and 2
6. (8d – 3 + 9d3) – (d3 – 13d2 – 4)
8d3 + 13d2 + 8d + 1
Find the difference
8d – 3 + 9d3 – d3 + 13d2 + 4
9d3 – d3 + 13d2 + 8d – 3 + 4
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.
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). 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
x2 -5x +4
2x
-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.
2x3
-5x2
-10x2
+25x
+8x
-20
Almost done!Go to
the next slide!
x2 -5x +4
2x
-5
Multiply (2x - 5)(x2 - 5x + 4) Combine like terms!
2x3
-5x2
-10x2
+25x
+8x
-20
2x3 – 15x2 + 33x - 20