Answer:
[tex]75k(x+4)(x+2)[/tex]
Step-by-step explanation:
The first expression is
[tex]25k^4+200k^3+400k^2[/tex]
First, we extract the greater common factor
[tex]25k^{2}(k^{2}+8k+16 )[/tex]
Second, we have the trinomial [tex]k^{2}+8k+16[/tex]
Notice that we need to find two number which product is 16 and which sum is 8, those numbers are 4 and 4.
So, the factors of the expression are
[tex]25k^4+200k^3+400k^2=25k^{2} (x+4)(x+4)=25k^{2}(x+4)^{2}[/tex]
The second expression is
[tex]15k^3+90k^2+120k[/tex]
We use the same process.
Extract the greatest common factor
[tex]15k(k^{2}+6k+8 )[/tex]
We solve the trinomial [tex]k^{2}+6k+8[/tex]. We need to find two numbers which product is 8 and which sum is 6, those numbers are 4 and 2.
[tex]15k^3+90k^2+120k=15k(x+2)(x+4)[/tex]
Now, the least common multiple is formed by factors that repeats in both expression.
Therefore, the least common multiple is [tex]75k(x+4)(x+2)[/tex], because the LCM between 25 and 15 is 75.
