The L.C.M. of (x^{2}-y^{2}),(x^{3}-y^{3}),and | vedclass

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(B) First,factorize each expression:$1. x^{2}-y^{2} = (x-y)(x+y)$$2. x^{3}-y^{3} = (x-y)(x^{2}+xy+y^{2})$$3. x^{3}-x^{2}y-xy^{2}+y^{3} = x^{2}(x-y)-y^

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$(x+y)(x-y)^{2}(x^{2}+y^{2}+xy)$

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(B) First,factorize each expression:$1. x^{2}-y^{2} = (x-y)(x+y)$$2. x^{3}-y^{3} = (x-y)(x^{2}+xy+y^{2})$$3. x^{3}-x^{2}y-xy^{2}+y^{3} = x^{2}(x-y)-y^{2}(x-y) = (x^{2}-y^{2})(x-y) = (x+y)(x-y)(x-y) = (x+y)(x-y)^{2}$To find the $L.C.M.$,take the highest power of each distinct factor present in the expressions:Factors are $(x+y)$,$(x-y)$,and $(x^{2}+xy+y^{2})$.The highest power of $(x+y)$ is $(x+y)^{1}$.The highest power of $(x-y)$ is $(x-y)^{2}$.The highest power of $(x^{2}+xy+y^{2})$ is $(x^{2}+xy+y^{2})^{1}$.Therefore,$L.C.M. = (x+y)(x-y)^{2}(x^{2}+xy+y^{2})$.

The $L.C.M.$ of $(x^{2}-y^{2})$,$(x^{3}-y^{3})$,and $(x^{3}-x^{2}y-xy^{2}+y^{3})$ is

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