There’s an easy trick to grow bigger quads and strengthen/tighten your core at the same time but you rarely see anyone doing it; probably because it sucks.
~12-15 rep front squat sets, ass to grass with no top lockout to keep stress on the quads. Keep feet about 12” apart and keep your feet pointed straight forward.
You aren’t turning the toes out to engage the glute/hip complex and the bar being in the front rack position keeps the back vertical so the hips can’t push as far back into a normal squat position. This means it’s predominately hitting the quads and a 12-15 rep set will set them on fire. I normally do these after the main lifts as an assistance exercise because they will definitely gas you.
If you’re feeling especially strong, you can try them all the way down, half up, back down, and all the way up = one rep. As always, progress with either reps or weight through a structured program
If your core is already gassed from the main movements of the day (as it sometimes is), I will substitute machine hack squats with low and close foot placement in lieu of front squats.
You will not get the same ab and lower back work in, but, it will toast the quads while allowing for more optimal recovery.