Binomial Theorem
guided notes
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The Binomial Theorem (long way) guided notes
A binomial is a _______________________
with ______ terms.
Rather than multiply the binomial times itself
many times, we can use the binomial theorem
as a short cut.
(2x+5) 3
STEP 1 : Draw blanks for ______________.
- The number of blanks is the _________________________________________________.
STEP 2 : Write the _________ term in the _________ blank.
- Be sure to raise it to the ___________________________ as the original problem.
- Continue to write term in the following blanks: ___________________ one from the exponent each time.
STEP 3 : ________________ 2nd term from original problem by each new term.
- Start with _______ exponent in first blank: ___________ one to exponent each time.
STEP 4 : Use _______________________________________.
- Use the nth row with n being the value of the __________________________________.
- Example: 4 blanks means use the _________ row. 8 blanks means use the _________ row.
© Ashley Andrews – Absolute Math, 2022
STEP 5 : Evaluate ___________________________.
- Be sure to raise all numbers and variables ________________________________ to the power.
STEP 6 : ___________________ constants to get new _______________________.
STEP 7 : Add _______________________ or _______________________ signs.
- If original problem is _______, use ________ signs.
- If original problem is _______, signs will alternate _________ then _________.
(𝑥 − 2𝑦)!
© Ashley Andrews – Absolute Math, 2022
The Binomial Theorem (long way) guided notes
POLYNOMIAL
A binomial is a _______________________
2
with ______
terms.
Rather than multiply the binomial times itself
many times, we can use the binomial theorem
as a short cut.
(2x+5) 3
TERMS
STEP 1 : Draw blanks for ______________.
EXPONENT PLUS ONE
- The number of blanks is the _________________________________________________.
EXPONENT IS 3, SO WE HAVE 4 BLANKS
1st
1st
STEP 2 : Write the _________
term in the _________
blank.
SAME POWER
- Be sure to raise it to the ___________________________
as the original problem.
SUBTRACT
- Continue to write term in the following blanks: ___________________
one from the exponent each time.
(2x)3
(2x)2
(2x)1
(2x)0
MULTIPLY
STEP 3 : ________________
2nd term from original problem by each new term.
ADD
0
- Start with _______
exponent in first blank: ___________
one to exponent each time.
(2x)3 (5)0
(2x)2 (5)1
(2x)1 (5)2
(2x)0 (5)3
PASCAL’S TRIANGLE
STEP 4 : Use _______________________________________.
EXPONENT PLUS ONE
- Use the nth row with n being the value of the __________________________________.
4
8
- Example: 4 blanks means use the _________
row. 8 blanks means use the _________
row.
th
(1) (2x)3 (5)0
(3) (2x)2 (5)1
th
(3) (2x)1 (5)2
(1) (2x)0 (5)3
© Ashley Andrews – Absolute Math, 2022
EXPONENTS
STEP 5 : Evaluate ___________________________.
INSIDE PARENTHESIS
- Be sure to raise all numbers and variables ________________________________
to the power.
(1) (2)3 (x)3 (5)0
(3) (2)2 (x)2 (5)1
(3) (2)1 (x)1 (5)2
(1) (2)0 (x)0 (5)3
(1) (8) (x)3 (1)
(3) (4) (x)2 (5)
(3) (2) (x)1 (25)
(1) (1) (1) (125)
MULTIPLY
COEFFICIENTS
STEP 6 : ___________________
constants to get new _______________________.
8x3
60x2
150x
125
ADDITION
SUBTRACTION
STEP 7 : Add _______________________
or _______________________
signs.
+
+
- If original problem is _______,
use ________
signs.
+
- If original problem is _______,
signs will alternate _________
then _________.
8x3
60x2
150x
125
(𝑥 − 2𝑦)!
(1) (x)5 (-2)0 (y)0
x5
(5) (x)4 (-2)1 (y)1
(10) (x)3 (-2)2 (y)2
(10) (x)2 (-2)3 (y)3
(5) (x)1 (-2)4 (y)4
(1) (x)0 (-2)5 (y)5
-10x4y
40x3y2
-80x2y3
80xy4
-32y5
243 – 810y + 1080y2 – 720y3 + 2400y4 – 32y5
© Ashley Andrews – Absolute Math, 2022