To simplify the expression [tex]\(4x\sqrt{3x} - x\sqrt{3x} - 2x\sqrt{3x}\)[/tex], follow these steps:
1. Identify Like Terms: Notice that each term in the expression contains [tex]\(x\sqrt{3x}\)[/tex]:
[tex]\[
4x\sqrt{3x}, \quad x\sqrt{3x}, \quad \text{and} \quad 2x\sqrt{3x}
\][/tex]
2. Combine Like Terms: We can factor out the common term [tex]\(x\sqrt{3x}\)[/tex] from each term:
[tex]\[
4x\sqrt{3x} - x\sqrt{3x} - 2x\sqrt{3x} = (4 - 1 - 2)x\sqrt{3x}
\][/tex]
3. Simplify Coefficients: Combine the numerical coefficients:
[tex]\[
4 - 1 - 2 = 1
\][/tex]
4. Express the Simplified Form: After combining the coefficients, we get:
[tex]\[
1x\sqrt{3x}
\][/tex]
Since multiplying by 1 does not change the expression, we can simplify it to:
[tex]\[
x\sqrt{3x}
\][/tex]
Thus, the simplified form of [tex]\(4x\sqrt{3x} - x\sqrt{3x} - 2x\sqrt{3x}\)[/tex] is:
[tex]\[
x\sqrt{3x}
\][/tex]
