Questions: (x^2-3x)(1+x)

Solution Steps

To simplify the expression \((x^{2}-3x)(1+x)\), we can use the distributive property to expand the expression. This involves multiplying each term in the first polynomial by each term in the second polynomial and then combining like terms.

We start with the expression \((x^{2}-3x)(1+x)\). Using the distributive property, we expand it as follows:

\[ (x^{2}-3x)(1+x) = x^{2}(1+x) - 3x(1+x) \]

Next, we distribute each term:

\[ x^{2}(1+x) = x^{2} + x^{3} \] \[ -3x(1+x) = -3x - 3x^{2} \]

Now, we combine the results from the distributions:

\[ x^{3} + x^{2} - 3x^{2} - 3x = x^{3} - 2x^{2} - 3x \]

Final Answer