How do you factor the trinomial $t^2 + 6tf - 16f^2$ ?

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Answer 1 · 2016-03-18T08:25:01

$(t-2f)(t+8f)$

If $at^2+btf+cf^2$ is the trinomial, we have to split $b$ in two parts, which add up to $b$ and whose product is $ac$ .

Here, in $t^2+6tf-16f^2$ , we will have to spit $6$ in two parts, so that the product of the two is $-16$ .

It is apparent that these are $+8$ and $-2$ and hence $t^2+6tf-16f^2$ can be written as

$t^2+8tf-2tf-16f^2$ or

= $t(t+8f)-2(t+8f)$ or

= $(t-2f)(t+8f)$

How do you factor the trinomial t^2 + 6tf - 16f^2t^2 + 6tf - 16f^2?