Question

for every natural number n,

(n+1)2 - n2 = ____
I will explain the statement above that is n plus 1 power of 2 minus power of 2 is equal to ____​

Answer 1

Answer:

2n+2-n² ........... ...

Answer 2

Concept:

Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. In order to compute algebraic expressions and solve various polynomials, algebraic identities are applied in this manner.

Identity I: (a + b)² = a² + 2ab + b²

Identity II: (a – b)² = a² – 2ab + b²

Identity III: a² – b²= (a + b)(a – b)

Identity IV: (x + a)(x + b) = x² + (a + b) x + ab

Identity V: (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

Identity VI: (a + b)³ = a³ + b³ + 3ab (a + b)

Identity VII: (a – b)³ = a³ – b³ – 3ab (a – b)

Identity VIII: a3 + b3 + c3 – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca)

Given:

(n+1)²-n²

Find:

Find the value of (n+1)²-n²

Solution:

(n+1)²-n²

= n²+2n+1-n²

=2n+1

or

(n+1)²-n²

Using the identity, a²-b²=(a+b)(a-b)

=(n+1+n)(n+1-n)

=(2n+1)(1)

=2n+1

Therefore, (n+1)²-n² is 2n+1

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