Question

factorise 16z⁴-72z²+81​

Answer 1

Step-by-step explanation:

$f(z)=16z^4-72z^2+81$

Let $z^2$ be $\alpha$

Now,

$f(\alpha ) =16\alpha^2-72\alpha +81$

$16\alpha^2-36\alpha -36\alpha+81\\4\alpha(4\alpha -9)-9(4\alpha -9)\\(4\alpha-9)(4\alpha-9)$

Substituting

$(4z^2-9)^2$ (Ans)