Question

What is the LCM of 5xy and 10y² ? ​

Answer 1

Answer:  10xy²

We can type 10xy^2 to mean the same thing.

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Explanation:

The LCM of the coefficients 5 and 10 is 10. Note how 5 is a factor of 10.

For the variable portions, you select the terms that are unique and have the highest exponent. We have an x term with exponent 1 and y term with exponent as high as 2. So that's why we go with xy² as the variable portion.

Overall, we end up with an LCM of 10xy²

Answer 2

(1): "y2" was replaced by "y^2". 1 more similar replacement(s).

STEP
1
:
Equation at the end of step 1

((5 • (x2)) - 5xy) - (2•5y2)
STEP
2
:

Equation at the end of step
2
:

(5x2 - 5xy) - (2•5y2)
STEP
3
:

STEP
4
:
Pulling out like terms

4.1 Pull out like factors :

5x2 - 5xy - 10y2 = 5 • (x2 - xy - 2y2)

Trying to factor a multi variable polynomial :

4.2 Factoring x2 - xy - 2y2

Try to factor this multi-variable trinomial using trial and error

Found a factorization : (x + y)•(x - 2y)

Final result :
5 • (x + y) • (x - 2y)