#$&*
MTH 158
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
Multiplying Polynomials
** **
Chapter R.4; Question 87.
** **
I know how to multiply two polynomials together but when we add the third one, I get lost. I've tried doing this problem several different ways and always come close to the answer but never exact. I can't figure out what I'm doing wrong for:
(2x + 1)^3
@&
We can start by saying that
(2x + 1)^ 3 = (2x + 1) * (2x + 1)^2
Now let's find (2x + 1)^2:
(2x+1)^2 = (2x + 1) * (2x + 1)
= 2x * ( 2x + 1) + 1 * (2x + 1)
= 4 x^2 + 2x + 2x + 1
= 4 x^2 + 4 x + 1.
So
(2x + 1)^ 3 = (2x + 1) * (2x + 1)^2
= (2x + 1) * ( 4 x^2 + 4 x + 1)
= 2x * ( 4 x^2 + 4 x + 1) + 1 * ( 4 x^2 + 4 x + 1)
= 8 x^3 + 8 x^2 + 2 x + 4 x^2 + 4 x + 1
= 8 x^3 + 8 x^2 + 4 x^2 + 2 x + 4 x + 1
= 8 x^3 + 12 x^2 + 6 x + 1.
*@
#$&*
MTH 158
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
Multiplying Polynomials
** **
Chapter R.4; Question 87.
** **
I know how to multiply two polynomials together but when we add the third one, I get lost. I've tried doing this problem several different ways and always come close to the answer but never exact. I can't figure out what I'm doing wrong for:
(2x + 1)^3
@&
We can start by saying that
(2x + 1)^ 3 = (2x + 1) * (2x + 1)^2
Now let's find (2x + 1)^2:
(2x+1)^2 = (2x + 1) * (2x + 1)
= 2x * ( 2x + 1) + 1 * (2x + 1)
= 4 x^2 + 2x + 2x + 1
= 4 x^2 + 4 x + 1.
So
(2x + 1)^ 3 = (2x + 1) * (2x + 1)^2
= (2x + 1) * ( 4 x^2 + 4 x + 1)
= 2x * ( 4 x^2 + 4 x + 1) + 1 * ( 4 x^2 + 4 x + 1)
= 8 x^3 + 8 x^2 + 2 x + 4 x^2 + 4 x + 1
= 8 x^3 + 8 x^2 + 4 x^2 + 2 x + 4 x + 1
= 8 x^3 + 12 x^2 + 6 x + 1.
*@
#$&*
MTH 158
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
Multiplying Polynomials
** **
Chapter R.4; Question 87.
** **
I know how to multiply two polynomials together but when we add the third one, I get lost. I've tried doing this problem several different ways and always come close to the answer but never exact. I can't figure out what I'm doing wrong for:
(2x + 1)^3
@&
We can start by saying that
(2x + 1)^ 3 = (2x + 1) * (2x + 1)^2
Now let's find (2x + 1)^2:
(2x+1)^2 = (2x + 1) * (2x + 1)
= 2x * ( 2x + 1) + 1 * (2x + 1)
= 4 x^2 + 2x + 2x + 1
= 4 x^2 + 4 x + 1.
So
(2x + 1)^ 3 = (2x + 1) * (2x + 1)^2
= (2x + 1) * ( 4 x^2 + 4 x + 1)
= 2x * ( 4 x^2 + 4 x + 1) + 1 * ( 4 x^2 + 4 x + 1)
= 8 x^3 + 8 x^2 + 2 x + 4 x^2 + 4 x + 1
= 8 x^3 + 8 x^2 + 4 x^2 + 2 x + 4 x + 1
= 8 x^3 + 12 x^2 + 6 x + 1.
*@
#$&*
MTH 158
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
Multiplying Polynomials
** **
Chapter R.4; Question 87.
** **
I know how to multiply two polynomials together but when we add the third one, I get lost. I've tried doing this problem several different ways and always come close to the answer but never exact. I can't figure out what I'm doing wrong for:
(2x + 1)^3
@&
We can start by saying that
(2x + 1)^ 3 = (2x + 1) * (2x + 1)^2
Now let's find (2x + 1)^2:
(2x+1)^2 = (2x + 1) * (2x + 1)
= 2x * ( 2x + 1) + 1 * (2x + 1)
= 4 x^2 + 2x + 2x + 1
= 4 x^2 + 4 x + 1.
So
(2x + 1)^ 3 = (2x + 1) * (2x + 1)^2
= (2x + 1) * ( 4 x^2 + 4 x + 1)
= 2x * ( 4 x^2 + 4 x + 1) + 1 * ( 4 x^2 + 4 x + 1)
= 8 x^3 + 8 x^2 + 2 x + 4 x^2 + 4 x + 1
= 8 x^3 + 8 x^2 + 4 x^2 + 2 x + 4 x + 1
= 8 x^3 + 12 x^2 + 6 x + 1.
*@