• Study Resource
• Explore

Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Fundamental theorem of algebra wikipedia, lookup

Factorization of polynomials over finite fields wikipedia, lookup

System of polynomial equations wikipedia, lookup

Big O notation wikipedia, lookup

Vincent's theorem wikipedia, lookup

Polynomial wikipedia, lookup

Transcript
```Combining Like
Polynomials and
Distributing
Tammy Wallace
Varina High
Term
A term is a number, variable, or the product of
numbers and variables.
number
5 is a ________________________________
variable
m is a _______________________________
the product of a number
and a variable.
2x² is _________________________________
Constant
A constant is a number add or subtracted to another
term.
5
__________ is the constant in 3x + 4y + 5
2
__________
is the constant in 2 – 3x
Coefficient
A coefficient is the numerical part multiplied in front of
a variable.
4 is the coefficient in front of 4a
______
1 is the coefficient in front of y²
______

______
is the coefficient in front of
5 2
7
Like Term
A like term is a term that has the same variable and
the same exponents.
13k and 22k
5ab and 4ba
3 2 and  2
Simplifying Expressions
To simplify an expression means to add or subtract the
coefficients of all like terms based on the operation in
front of each term.
Simplify 3x + 6x
Because both terms have the same variables which
x
are ________,
they are like terms and can be simplified
equal to
9x
Simplify 8x² + 2x² + 5y + y
Are there any like terms?
Yes
Which ones?
8x² is a like term with 2x²
and
5y is a like term with y
Therefore, once combined, the expression is simplified
to
10x² + 6y
Simplify
1) 5a + 7a
12a
2) 6.1y - 3.2y
2.9y
3) 4x2y + x2y
5x2y
4) 3m2n + 10mn2 + 7m2n - 4mn2
10m2n + 6mn2
5) 13a + 8a + 6b
21a + 6b
6) 4d + 6a2 - d + 12a2
18a2 + 3d
3y
y
7)

4
4
y
Which of the following is the simplified
form of
5x - 4 - 7x + 14 ?
1.
2.
3.
4.
-12x + 10
-2x + 10
2x - 18
12x – 18
Polynomial
A polynomial is a group of two or more terms.
(9y - 7x + 15a) + (-3y + 8x - 8a)
Group your like terms and simplify
9y - 3y - 7x + 8x + 15a - 8a
6y + x + 7a
(3a2 + 3ab - b2) + (4ab + 6b2)
3a2 + 3ab + 4ab - b2 + 6b2
2
2
3a + 7ab + 5b
Subtracting Polynomials
Subtracting polynomials is a little different.
When subtracting polynomials, change the
subtraction sign to _____________
SECOND polynomials to its ______________.
opposite sign
signs in the _________
Subtract the following polynomials:
(9y - 7x + 15a) - (-3y + 8x - 8a)
opposite.
(9y - 7x + 15a) + (+ 3y - 8x + 8a)
Group the like terms.
9y + 3y - 7x - 8x + 15a + 8a
12y - 15x + 23a
5. Subtract the following polynomials:
(7a - 10b) - (3a + 4b)
opposite.
(7a - 10b) + (- 3a - 4b)
Group the like terms.
7a - 3a - 10b - 4b
4a - 14b
Find the sum or difference.
(5a – 3b) + (2a + 6b)
1.
2.
3.
4.
3a – 9b
3a + 3b
7a + 3b
7a – 3b
Find the sum or difference.
(5a – 3b) – (2a + 6b)
1.
2.
3.
4.
3a – 9b
3a + 3b
7a + 3b
7a – 9b
Distributive Property
The Distributive Property is the process of multiplying a
number directly outsides of the parenthesis by
everything inside the parenthesis.
Example
5(x + 7)
5•x+5•7
5x + 35
Distribute
3(m - 4)
3•m-3•4
3m - 12
Distribute
-2(y + 3)
-2 • y + (-2) • 3
-2y + (-6)
-2y - 6
Distribute
2(x² + 4x²y) + 5(3x² - x²y)
2x² + 8x²y + 15x² - 5x²y
2x² + 15x² + 8x²y – 5x²y
10x² +10x²y
Distribute
4(3y² + 4x²y) + (3y² - xy²)
12y² + 16x²y + 3y² - xy²
12y² + 3y² + 16x²y – xy²
15y² + 16x²y – xy²
Distribute
3(3a² + 12) - 2(a² - 1)
9a² + 36 - 2a² + 2
9a² - 2a² + 36 + 2
7a² + 38
Distribute
2(3x² - 6y² + 4x²y) - (3x² + y² - x²y)
6x² - 12y² + 8x²y - 3x² - y² + x²y
6x² - 3x² -12y² - y² + 8x²y + x²y
3x² -13y² + 9x²y
```
Related documents