Question

find the LCM : x2-y2 , x2+2xy+yand x2
+xy​

Answer 1

Answer:

xy(x+Y)

Step-by-step explanation:

We know that the least common multiple (LCM) is the smallest number or expression that is a common multiple of two or more numbers or algebraic terms.

We first factorize the given binomials x

2

y+xy

2

and x

2

+xy as shown below:

x

2

y+xy

2

=xy(x+y)

x

2

+xy=x(x+y)

Now multiply all the factors, using each common factor only once, therefore, the LCM is:

x×y×(x+y)=xy(x+y)

Hence, the LCM of x

2

y+xy

2

and x

2

+xy is xy(x+y).