Question

Factorise a^4 - 16b^4

Answer 1

here's your answer.......

Answer 2

Given:

An algebraic expression a^4 - 16b^4.

To Find:

The factorized form of the given expression is?

Solution:

1. The identity used to solve the given expression is:

• (a²-b²)  = (a+b)(a-b)

2. Using the above identity the expression can be factorized,

=> $(a^4-16b^4) = (a^2+4b^2)(a^2-4b^2)$, ( Using the identity )

=> The term (a²- 4b²) can be furtherly simplified,

=>    $(a^4-16b^4) = (a^2+4b^2)(a+2b)(a-2b)$, ( Using the identity ).

Therefore, the factorized form of the expression (a^4-b^4) is (a²+4b²)(a+2b)(a-2b).