How do I find the binomial expansion of (2x+1)^3 ?

Francisca Rodden

Francisca Rodden

Answered question

2021-12-26

How do I find the binomial expansion of (2x+1)3 ?

Answer & Explanation

eninsala06

eninsala06

Beginner2021-12-27Added 37 answers

We must use our knowledge of the binomial expansion:
Method 1:
We can use:
(x+1)n=1+nx+n(n1)2!x2+n(n1)(n2)3!x3+
Substituting n=3 and x for 2x
(2x+1)3=1+(32x)+322!(2x)2+3213!(2x)3
=1+6x+12x2+8x3
ramirezhereva

ramirezhereva

Beginner2021-12-28Added 28 answers

Method 2:
We can use:
(A+B)n=An+(n1)An1B1+(n2)An2B2+
Letting A=2x and B=1 for this circumstance:
(2x+1)3=(2x)3+(31)(2x)2(1)+(32)(2x)1(1)2+(33)(2x)0(1)3
=8x3+12x2+6x+1
nick1337

nick1337

Expert2022-01-08Added 777 answers

Explanation:
we use Pascal's triangle for the coefficients
(a+b)21,2,1
(a+b)31,3,3,1
So we need 1,3,3,1
the powers of the terms will sum to 3
and startingthe first term will be 3 and descend in 1 s thus
(2x+1)3=1(2x)3+3(2x)2(1)+3(2x)(1)2+113
(2x+1)3=8x3+12x2+6x+1

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