Question

Factor by using the perfect-square trinomial: $64{\mathrm{x}}^2-144\mathrm{x}+81$

Answer 1

Factorize the given polynomial:

The given trinomial $64{\mathrm{x}}^2-144\mathrm{x}+81$can be written as ${\left(8\mathrm{x}\right)}^2-2\times 8\mathrm{x}\times 9+{\left(9\right)}^2$

We know that, ${\mathrm{a}}^2-2\mathrm{ab}+{\mathrm{b}}^2={\left(\mathrm{a}-\mathrm{b}\right)}^2$

Here, $\mathrm{a}=8\mathrm{x}$ and $\mathrm{b}=9$

$\therefore {\left(8\mathrm{x}\right)}^2-2\times 8\mathrm{x}\times 9+{\left(9\right)}^2=$${\left(8\mathrm{x}-9\right)}^2$

Hence, the required factorization of $64{\mathrm{x}}^2-144\mathrm{x}+81$ is ${\left(8\mathrm{x}-9\right)}^2$.