To simplify the given expression [tex]\( 5x\sqrt{3x} - 2x\sqrt{3x} - x\sqrt{3x} \)[/tex], let's proceed step-by-step:
1. Identify Like Terms:
Notice that all terms in the expression contain [tex]\( x\sqrt{3x} \)[/tex]. Therefore, they can be combined by factoring [tex]\( x\sqrt{3x} \)[/tex] out.
2. Combine the Coefficients:
- The first term is [tex]\( 5x\sqrt{3x} \)[/tex]. The coefficient here is 5.
- The second term is [tex]\( -2x\sqrt{3x} \)[/tex]. The coefficient here is -2.
- The third term is [tex]\( -x\sqrt{3x} \)[/tex]. The coefficient here is -1 (since [tex]\( x\sqrt{3x} \)[/tex] is equivalent to [tex]\( 1 \cdot x\sqrt{3x} \)[/tex]).
Combine the coefficients:
[tex]\[
5 - 2 - 1
\][/tex]
3. Calculate the Sum of Coefficients:
[tex]\[
5 - 2 = 3
\][/tex]
[tex]\[
3 - 1 = 2
\][/tex]
4. Rewrite the Expression:
Now substitute the combined coefficient back into the expression [tex]\( x\sqrt{3x} \)[/tex]:
[tex]\[
(5 - 2 - 1)x\sqrt{3x} = 2x\sqrt{3x}
\][/tex]
Therefore, the simplified form of the given expression [tex]\( 5x\sqrt{3x} - 2x\sqrt{3x} - x\sqrt{3x} \)[/tex] is [tex]\( \boxed{2x\sqrt{3x}} \)[/tex].
