Can someone check my answer please?

How does the antibiotic penicillin kill bacterial cells? Is it more effective against gram positive or gram negative organisms? Explain.

Most bacteria produce a cell wall that is composed partly of a macromolecule called peptidoglycan, made up of amino sugars and short peptides. Penicillin, one of the first antibiotics to be used widely, prevents the final cross-linking step, or transpeptidation, in assembly of this macromolecule. The result is a very fragile cell wall that bursts, killing the bacterium. In other worlds, â-lactam antibiotics work by inhibiting the formation of peptidoglycan cross links in the bacterial cell wall. The â-lactam moiety of penicillin binds to the enzyme (transpeptidase) that links the peptidoglycan molecules in bacteria, and this weakens the cell wall of the bacterium when it multiplies (in other words, the antibiotic causes cytolysis or death when the bacterium tries to divide). Antibiotic penicillin is more effective against gram-positive organisms because…..