Factor a^2-24am^2x^2+144m^4x^4

$a^{2} - 24 a m^{2} x^{2} + 144 m^{4} x^{4}$

Rewrite $144 m^{4} x^{4}$ as ${(12 m^{2} x^{2})}^{2}$ .

$a^{2} - 24 a m^{2} x^{2} + {(12 m^{2} x^{2})}^{2}$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$24 a m^{2} x^{2} = 2 \cdot a \cdot (12 m^{2} x^{2})$

Rewrite the polynomial.

$a^{2} - 2 \cdot a \cdot (12 m^{2} x^{2}) + {(12 m^{2} x^{2})}^{2}$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = a$ and $b = 12 m^{2} x^{2}$ .

${(a - 12 m^{2} x^{2})}^{2}$