Question

factor by using the perfect - square trinomial formula.\\(49x^{2}-126x + 81\\)\\(49x^{2}-126x + 81=square\\)

Explanation:

Step1: Identify perfect square terms

$49x^2=(7x)^2$, $81=9^2$

Step2: Verify middle term condition

Check if $2ab=2\times7x\times9=126x$, matches the trinomial's middle term (with negative sign, since the trinomial is $a^2-2ab+b^2$)

Step3: Apply perfect square formula

Use $a^2-2ab+b^2=(a-b)^2$, substitute $a=7x$, $b=9$

Answer:

$(7x-9)^2$