Question

factorise using algebraic identity 16a^4-b^4

Answer 1

$\textbf {ANSWER:}$

The identity to be used:
${x}^{2} - {y}^{2} = (x -y)(x + y)$


$16 {a}^{4} - {b}^{4} = {(4 {a}^{2} )}^{2} - {( {b}^{2}) }^{2} \\ = >( 4 {a}^{2} - {b}^{2} )(4 {a}^{2} + {b}^{2} )$

Answer 2

16a^4-b^4=(4a²)²-(b²)²=(4a²+b²)(4a²-b²)   (using x²-y²=(x+y)(x-y))

((2a)²+(b)²)((2a)²-(b)²)=((2a)²+(b)²)(2a+b)(2a-b)

=((2a+b)²-4ab)(2a+b)(2a-b)(using (x+y)²=x²+y²+2xy )