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Question

Factorise : $$ 16x^4 -1 $$


Solution

Given : $$ 16x^4 -1 $$
We can further write it as
$$ 16x^4 -1 $$$$ =(4x^2)^2 -1^2 $$
Based on the equation $$ a^2-b^2=(a+b)(a-b) $$
We get,
$$ 16x^4 -1 $$$$ =(4x^2 +1)(4x^2 -1) $$
On further simplification using the formula
$$ 16x^4 -1 $$$$ =(4x^2+1)((2x)^2 -1^2 ) $$
So we get,
$$ 16x^4 -1 $$$$ =(4x^2 +1)(2x+1)(2x-1) $$

Mathematics
RS Agarwal
Standard IX

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