Multiplying Monomials worksheet with 30 problems for simplifying algebraic expressions.

I will solve the first problem from the worksheet as an example.

Problem: Simplify $-1x^2y^3z \times 2x$

Step 1: Separate the numbers and the variables.
We have two parts to multiply:
1. The coefficients (numbers): $-1$ and $2$
2. The variables: $x^2y^3z$ and $x$

Step 2: Multiply the coefficients.
$-1 \times 2 = -2$

Step 3: Multiply the variables.
- For $x$: We have $x^2$ and $x$ (which is $x^1$). When multiplying variables with exponents, we add the exponents.
$x^2 \times x^1 = x^{2+1} = x^3$
- For $y$: We only have $y^3$, so it stays $y^3$.
- For $z$: We only have $z$, so it stays $z$.

Step 4: Combine everything.
Put the new coefficient and the new variables together:
$-2x^3y^3z$

Final Answer:
-2x^3y^3z