For the production of sum and difference frequencies with no real multiplier accuracy, just operate the transistor bias in a non-linear part of the transconductance curve. That would be near saturation or near cutoff. Most mixers use them near cutoff, the more efficient (less power) option.How 2 signals can multiplies using transistor as active component, say the 2 signals to be multiplied are one with frequency=1KHz and other with freq=1MHz.
Like the pulsating of two sounds just barley out of frequency I'm guessing.You need to understand a circuit called a doubly balanced mixer. It multiplies two signals together and produces components at the original two frequencies, (1 kHz, 1 MHz.). It also produces components that are the sum and difference of the two frequencies. These are called the upper and lower sidebands. They are at 1.001 MHz. and at 0.999 MHz.
Now, for the $64,000 question -- what happens when you run the upper sideband at 1.001 MHz. and local oscillator of 1.000 MHz. through the multiplier? What comes out?