Question

factorise the term a⁶-b⁶​

Answer 1

Answer:

(a-b)^6

Step-by-step explanation:

Hope it helps!!

Answer 2

Answer:

a⁶ - b⁶ = (a² - b²)(a² + ab + b²)(a² - ab + b²)

Step-by-step explanation:

We have,

a⁶ - b⁶

But we can also write it as,

(a³)² - (b³)²

Using the identity,

x² - y² = (x + y)(x - y)

So,

(a³)² - (b³)²

= (a³ + b³)(a³ - b³)

Using the identity,

x³ + y³ = (x + y)(x² - xy + y²)

x³ - y³ = (x - y)(x² + xy + y²)

So,

= (a³ + b³)(a³ - b³)

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

Since Multiplication is Associative,

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

Using the identity,

(x + y)(x - y) = x² - y²

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

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

Hence,

a⁶ - b⁶ = (a² - b²)(a² + ab + b²)(a² - ab + b²)

Hope it helped and believing you understood it. All the best.