Question

Solve using identities with reasons
(x+1)(x-1)(x2+1)​

Answer 1

Given expression,

 (x+1)*(x-1)*(x²+1)

=[(x+1)*(x-1)]*(x²+1)

Using formula (a=b)*(a-b)=a²-b²

Substituting x in place of a and 1 in place of b

Therefore,

 (x+1)*(x-1)

=(x)²-(1)²

 =x²-1

Therefore,

 [(x+1)*(x-1)]*(x²+1)

=[x²-1]*(x²+1) 

=(x²-1)(x²+1)

Using formula

(a=b)*(a-b)=a²-b²

Substituting x² in place of a and 1 in place of b,

Therefore,

 (x²-1)*(x²+1)

=(x²)²-(1)²

= x⁴-1

   

Answer 2

Answer:

$\mathfrak\red{Heya}$

Step-by-step explanation:

$Consider\:the\:Given\:Expression$

⇒ $[tex](x+1)(x-2)(x^{2} -1)$

We know that $(a+b)(a-b)=a^{2}- b^{2}$

Here $a=x,b=1$

∴ $(x+1)(x-1)=x^{2} -1^{2} =x^{2} -1$

∴ $(x+1)(x-1)(x^{2} -1)=(x^{2} -1)(x^{2} +1)$

Here $a=x^{2} ,b=1$

$Again\:Applying\:the\:Same\:Identity$

We,Have

$(x+1)(x-1)(x^{2} -1)=(x^{2}) ^{2} -1^{2} )</p><p>=> x^{4} -1$