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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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^

Vedclass · Accepted Answer

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

Vedclass · Answer

(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

Similar Questions

Find the $G.C.D.$ of $8(x^{3}-x^{2}+x)$ and $28(x^{3}+1)$.

The $H.C.F.$ (Highest Common Factor) of two polynomials is $(y-7)$ and their $L.C.M.$ is $y^{3}-10y^{2}+11y+70$. If one of the polynomials is $y^{2}-5y-14$,find the other.

Find the $G.C.D.$ of $8(x^{4}-16)$ and $12(x^{3}-8)$.

If $(x-a)$ is the $G.C.D.$ of $x^{2}-x-6$ and $x^{2}+3x-18$,find the value of $a$.

The $L.C.M.$ and $H.C.F.$ of two polynomials $p(x)$ and $q(x)$ are $36 x^{3}(x+a)(x^{3}-a^{3})$ and $x^{2}(x-a)$ respectively. If $p(x)=4 x^{2}(x^{2}-a^{2})$,find $q(x)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module