Question

why we can not write it as....(.see the highlighted red part)
if no then why??
irrelevant answers will be reported
^_^

Answer 1

Answer :

Now, a⁶ - b⁶

= (a²)³ - (b²)³

= (a² - b²) {(a²)² + a²b² + (b²)²}

= (a + b) (a - b) (a⁴ + a²b² + b⁴) ...(i)

Again, a⁴ + a²b² + b⁴

= (a⁴ + 2a²b² + b⁴) - a²b²

= (a² + b²)² - (ab)²

= (a² + b² + ab) (a² + b² - ab)

From (i), we get

a⁶ - b⁶

= (a + b) (a - b) (a⁴ + a²b² + b⁴)

= (a + b) (a - b) (a² + b² + ab) (a² + b² - ab)

= (a - b) (a + b) (a² + ab + b²) (a² - ab + b²)

which is the required factorization.



#MarkAsBrainliest

Answer 2

Bonjour!

a^6 - b^6 = (a²)³ - (b²)³

= (a² - b²)((a²)² + a²b² + (b²)²)

= (a - b)(a + b)(a⁴ + a²b² + b⁴)

= (a - b)(a + b)(a⁴ + b²(a² + b²))

= (a - b)(a + b)(a² - ab + b²)(a² + ab + b²)

So, we get the same result by solving with a different method so we can write;

a^6 - b^6 = (a³)² - (b³)² or (a²)³ - (b²)³

Hope this helps...:)