Question

a^4 - 625

factorise it

Answer 1

Answer:

(a² + 25)(a + 5)(a - 5)

Step-by-step explanation:

Given Equation is a⁴ - 625

= (a)⁴ - (5)⁴

= (a²)² - (5²)²

We know that a² - b² = (a + b)(a - b)

= (a² + 5²)(a² - 5²)

= (a² + 5²)(a + 5)(a - 5)

= (a² + 25)(a + 5)(a - 5).

Hope it helps!

Answer 2

we have,

a⁴ - 625 = ${a}^{4} - {5}^{4}$

we know,

a²- b² = (a + b) ( a- b ).

thus,

expression in the question can be written as :-

${ {(a}^{2} )}^{2} - { ({5}^{2} )}^{2}$

$( {a}^{2} + 25) \times ( {a}^{2} - 25)$

again, (a² - 25) can be written as (a + 5) (a - 5).

So, final answer is :-

$( {a}^{2} + 25) \times (a + 5) \times (a - 5)$

Thanks

KSHITIJ