Question

Simplify using algebraic identity:

(p + q)(p^2 + q^2)(p^4 + q^4)(p - q).​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given:-

(p + q)(p^2 + q^2)(p^4 + q^4)(p - q).

To find:-

Simplify using algebraic identity:

(p + q)(p^2 + q^2)(p^4 + q^4)(p - q).

Solution:-

Given expression is

(p + q)(p^2 + q^2)(p^4 + q^4)(p - q).

=>[(p+q)(p-q)](p²+q²)(p⁴+q⁴)

(since (a+b)(a-b)=a²-b²)

=>(p²-q²)(p²+q²)(p⁴+q⁴)

=>[(p²-q²)(p²+q²)](p⁴+q⁴)

(since (a+b)(a-b)=a²-b²)

=>[(p²)²-(q²)²](p⁴+q⁴)

=>(p⁴-q⁴)(p⁴+q⁴)

(since (a+b)(a-b)=a²-b²)

=>(p⁴)²-(q⁴)²

(since (a^m)^n=a^mn)

=>(p⁴ײ)-(q⁴ײ)

=>p⁸-q⁸

Answer:-

(p + q)(p^2 + q^2)(p^4 + q^4)(p - q)=p⁸-q⁸

Used formulae:-

• (a+b)(a-b)=a²-b²
• (a^m)^n=a^mn