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Prove polynomial identities

Next Problem

Is the following proof valid? If not, what is the invalid step in the proof?


		$~~~~(4x-3)(x-2)^2$
Step $1$		$=(4x-3)(x-2)(x-2)$
Step $2$		$=(4x-3)(x^2-2x-2x+4)$
Step $3$		$=(4x-3)(x^2-4x+4)$
Step $4$		$=4x^3-16x^2+16x-3x^2-12x-12$
Step $5$		$=4x^3-19x^2+4x-12$