Question

22. The value of x6 - y6 is -​

Answer 1

Step-by-step explanation:

Given :-

x⁶-y⁶

To find:-

The value of x⁶- y⁶

Solution:-

Given expression is x⁶-y⁶

=>(x²)³-(y²)³

it is in the form of a³-b³

where a=x² and b= y²

a³-b³=(a-b)(a²+ab+b²)

=>(x²)³-(y²)³

=>(x²-y²)[(x²)²+x²y²+(y²)²]

=>(x²-y²)(x⁴+x²y²+y⁴)

=>(x+y)(x-y)(x⁴+x²y²+y⁴)

(or)

Given expression is x⁶-y⁶

=>(x³)²-(y³)²

This is in the form of a²-b²

where a=x³ and b=y³

a²-b²=(a+b)(a-b)

=>(x³+y³)(x³-y³)

We know that

a³+b³=(a+b)(a²-ab+b²)

a³-b³=(a-b)(a²+ab+b²)

=>(x+y)(x²-xy+y²)(x-y)(x²+xy+y²)

=>(x+y)(x-y)(x²+y²+xy)(x²+y²-xy)

=>(x+y)(x-y)[(x²+y²)²-(xy)²]

=>(x+y)(x-y)(x⁴+2x²y²+y⁴-x²y²)

=>(x+y)(x-y)(x⁴+x²y²+y⁴)

Answer:-

x⁶-y⁶= (x+y)(x-y)(x⁴+x²y²+y⁴)

Used formulae:-

• a³+b³=(a+b)(a²-ab+b²)

• a³-b³=(a-b)(a²+ab+b²)

• (a+b)(a-b)=a²-b²

• (a^m)^n=a^mn

• x⁶=x^(2×3)=(x²)³=(x³)²

• y⁶=y^(2×3)=(y²)³=(y³)²

• (a+b)²=a²+2ab+b²