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7.5 – Adding & Subtracting Polynomials. “Combining Like Terms” -. “Combining Like Terms” - ???. “Combining Like Terms” - ??? - Only if have exact same variables with exact same exponents on those variables!!!. “Combining Like Terms” - ??? - PowerPoint PPT Presentation
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7.5 – Adding & Subtracting Polynomials
“Combining Like Terms” -
“Combining Like Terms” - ???
“Combining Like Terms” - ???
- Only if have exact same variables with exact same exponents on those variables!!!
“Combining Like Terms” - ???
- Only if have exact same variables with exact same exponents on those variables!!!
“Combining Like Terms” - ???
- Only if have exact same variables with exact same exponents on those variables!!!
“Combining Like Terms” - ???
- Only if have exact same variables with exact same exponents on those variables!!!
“Combining Like Terms” - ???
- Only if have exact same variables with exact same exponents on those variables!!!
“Combining Like Terms” - ???
- Only if have exact same variables with exact same exponents on those variables!!!
Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5).
“Combining Like Terms” - ???
- Only if have exact same variables with exact same exponents on those variables!!!
Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5).
(3x2 – 4x + 8) + (2x – 7x2 – 5)
“Combining Like Terms” - ???
- Only if have exact same variables with exact same exponents on those variables!!!
Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5).
(3x2 – 4x + 8) + (2x – 7x2 – 5)
3x2 – 4x + 8 + 2x – 7x2 – 5
“Combining Like Terms” - ???
- Only if have exact same variables with exact same exponents on those variables!!!
Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5).
(3x2 – 4x + 8) + (2x – 7x2 – 5)
3x2 – 4x + 8 + 2x – 7x2 – 5
“Combining Like Terms” - ???
- Only if have exact same variables with exact same exponents on those variables!!!
Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5).
(3x2 – 4x + 8) + (2x – 7x2 – 5)
3x2 – 4x + 8 + 2x – 7x2 – 5
3x2 – 7x2
“Combining Like Terms” - ???
- Only if have exact same variables with exact same exponents on those variables!!!
Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5).
(3x2 – 4x + 8) + (2x – 7x2 – 5)
3x2 – 4x + 8 + 2x – 7x2 – 5
3x2 – 7x2
“Combining Like Terms” - ???
- Only if have exact same variables with exact same exponents on those variables!!!
Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5).
(3x2 – 4x + 8) + (2x – 7x2 – 5)
3x2 – 4x + 8 + 2x – 7x2 – 5
3x2 – 7x2 – 4x + 2x
“Combining Like Terms” - ???
- Only if have exact same variables with exact same exponents on those variables!!!
Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5).
(3x2 – 4x + 8) + (2x – 7x2 – 5)
3x2 – 4x + 8 + 2x – 7x2 – 5
3x2 – 7x2 – 4x + 2x
“Combining Like Terms” - ???- Only if have exact same variables with
exact same exponents on those variables!!!
Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5). (3x2 – 4x + 8) + (2x – 7x2 – 5) 3x2 – 4x + 8 + 2x – 7x2 – 5 3x2 – 7x2 – 4x + 2x + 8 – 5
“Combining Like Terms” - ???- Only if have exact same variables with
exact same exponents on those variables!!!
Ex. 1 Find (3x2 – 4x + 8) + (2x – 7x2 – 5). (3x2 – 4x + 8) + (2x – 7x2 – 5) 3x2 – 4x + 8 + 2x – 7x2 – 5 3x2 – 7x2 – 4x + 2x + 8 – 5
– 4x2 – 2x + 3
Ex. 2 Find (3n2 + 13n3 + 5n) – (7n + 4n3).
Ex. 2 Find (3n2 + 13n3 + 5n) – (7n + 4n3).
Ex. 2 Find (3n2 + 13n3 + 5n) – (7n + 4n3).
3n2 + 13n3 + 5n – 7n
Ex. 2 Find (3n2 + 13n3 + 5n) – (7n + 4n3).
3n2 + 13n3 + 5n – 7n – 4n3
Ex. 2 Find (3n2 + 13n3 + 5n) – (7n + 4n3).
3n2 + 13n3 + 5n – 7n – 4n3
Ex. 2 Find (3n2 + 13n3 + 5n) – (7n + 4n3).
3n2 + 13n3 + 5n – 7n – 4n3
13n3 – 4n3 + 3n2 + 5n – 7n
Ex. 2 Find (3n2 + 13n3 + 5n) – (7n + 4n3).
3n2 + 13n3 + 5n – 7n – 4n3
13n3 – 4n3 + 3n2 + 5n – 7n 9n3 + 3n2 – 2n
Ex. 2 Find (3n2 + 13n3 + 5n) – (7n + 4n3).
3n2 + 13n3 + 5n – 7n – 4n3
13n3 – 4n3 + 3n2 + 5n – 7n 9n3 + 3n2 – 2n
Ex. 3
From 1990 through 1999, the female population F and the male population M of the United States (in thousands) are modeled by the following equations, where n is the number of years since 1990.
F = 1247n + 126,971 M = 1252n + 120,741
a. Find an equation that models the total population T in thousands of the United States for this time period.
a. Find an equation that models the total population T in thousands of the United States for this time period.
T = female + male
a. Find an equation that models the total population T in thousands of the United States for this time period.
T = female + male
T = F + M
a. Find an equation that models the total population T in thousands of the United States for this time period.
T = female + male
T = F + M
a. Find an equation that models the total population T in thousands of the United States for this time period.
T = female + male
T = F + M
T = (1247n + 126,971)
a. Find an equation that models the total population T in thousands of the United States for this time period.
T = female + male
T = F + M
T = (1247n + 126,971)
a. Find an equation that models the total population T in thousands of the United States for this time period.
T = female + male
T = F + M
T = (1247n + 126,971)+(1252n + 120,741)
a. Find an equation that models the total population T in thousands of the United States for this time period.
T = female + male
T = F + M
T = (1247n + 126,971)+(1252n + 120,741)
T = 1247n + 126,971 + 1252n + 120,741
a. Find an equation that models the total population T in thousands of the United States for this time period.
T = female + male
T = F + M
T = (1247n + 126,971)+(1252n + 120,741)
T = 1247n + 126,971 + 1252n + 120,741
T = 1247n + 1252n + 126,971 + 120,741
a. Find an equation that models the total population T in thousands of the United States for this time period.
T = female + male
T = F + M
T = (1247n + 126,971)+(1252n + 120,741)
T = 1247n + 126,971 + 1252n + 120,741
T = 1247n + 1252n + 126,971 + 120,741
T = 2499n + 247,712
a. Find an equation that models the total population T in thousands of the United States for this time period.
T = female + maleT = F + M
T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126,971 + 1252n + 120,741T = 1247n + 1252n + 126,971 + 120,741
T = 2499n + 247,712b. If this trend continues, what will the
population of the United States Be in 2010?
a. Find an equation that models the total population T in thousands of the United States for this time period.
T = female + maleT = F + M
T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126,971 + 1252n + 120,741T = 1247n + 1252n + 126,971 + 120,741
T = 2499n + 247,712b. If this trend continues, what will the
population of the United States Be in 2010?T = 2499n + 247,712
a. Find an equation that models the total population T in thousands of the United States for this time period.
T = female + maleT = F + M
T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126,971 + 1252n + 120,741T = 1247n + 1252n + 126,971 + 120,741
T = 2499n + 247,712b. If this trend continues, what will the
population of the United States Be in 2010?T = 2499n + 247,712
n = 2010 – 1990 = 20
a. Find an equation that models the total population T in thousands of the United States for this time period.
T = female + maleT = F + M
T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126,971 + 1252n + 120,741T = 1247n + 1252n + 126,971 + 120,741
T = 2499n + 247,712b. If this trend continues, what will the population
of the United States Be in 2010?T = 2499n + 247,712
n = 2010 – 1990 = 20T = 2499(20) + 247,712
a. Find an equation that models the total population T in thousands of the United States for this time period.
T = female + maleT = F + M
T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126,971 + 1252n + 120,741T = 1247n + 1252n + 126,971 + 120,741
T = 2499n + 247,712b. If this trend continues, what will the population
of the United States Be in 2010?T = 2499n + 247,712
n = 2010 – 1990 = 20T = 2499(20) + 247,712T = 297,692
a. Find an equation that models the total population T in thousands of the United States for this time period.
T = female + maleT = F + M
T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126,971 + 1252n + 120,741T = 1247n + 1252n + 126,971 + 120,741
T = 2499n + 247,712b. If this trend continues, what will the population
of the United States Be in 2010?T = 2499n + 247,712
n = 2010 – 1990 = 20T = 2499(20) + 247,712T = 297,692 (thousand)
a. Find an equation that models the total population T in thousands of the United States for this time period.
T = female + maleT = F + M
T = (1247n + 126,971)+(1252n + 120,741) T = 1247n + 126,971 + 1252n + 120,741T = 1247n + 1252n + 126,971 + 120,741
T = 2499n + 247,712b. If this trend continues, what will the population
of the United States Be in 2010?T = 2499n + 247,712
n = 2010 – 1990 = 20T = 2499(20) + 247,712T = 297,692 (thousand)T = 297,692,000
