Question

Multiply:

Answer 1

\[\frac{ k+3 }{ 4k-2 } \times (12k^2+2k-4)\]
Now, this is what could call "multiplying polynomials" though these only contain one variable, this being "k".
In order to make this multiplication we will resort to the multiplication of fraction and you will notice, that any number or expression can be expressed as a fraction in order to make the multiplication easier.
Being this "multiplication of fraction, the product of numerators and denominator which is mathematically noted: \[\frac{ x }{ y } \times \frac{ a }{ b }=\frac{ xa }{ yb }\]
We will take this identity and utilize it to multiply the expressions, but first, notice that we can express \(12k^2+2k-4\) as \(\frac{ 12k^2+2k-4 }{ 1 }\) which is now a fraction:
\[\frac{ k+3 }{ 4k-2 } \times (12k^2+2k-4) \iff \frac{ k+3 }{ 4k-2 }\times \frac{ 12k^2+2k-4 }{ 1 }\]
Utilizing the multiplication of fractions:
\[\frac{ (k+3)(12k^2+2k-4) }{ (4k-2)(1) }\]
Now, let's utilize the distributive property in the numerator, which I must suppose you already know about at this point:
\[\frac{ 12k^2(k+3)+2k(k+3)-4(k+3) }{ 4k-2 }\]
I'll let you take over from here, just apply the distributive property again for each of those terms and you'll be golden.