Compound Integral Expressions.

2. Multiply $2a+3-4a^2$ by $3-2a^2-3a$.

Arrange both multiplicand and multiplier according to the ascending powers of $a$. $$\begin{gathered} r*4cr3\&+\&2a\&-\&4a^2\&\&\&\& \\ 3\&-\&3a\&-\&2a^2\&\&\&\& \\ \mathrm{\backslash cline}1-59\&+\&6a\&-\&12a^2\&\&\&\& \\ \&-\&9a\&-\&6a^2\&+\&12a^3\&\& \\ \&\&\&-\&6a^2\&-\&4a^3\&+\&8a^4 \\ \mathrm{\backslash hline}9\&-\&3a\&-\&24a^2\&+\&8a^3\&+\&8a^4 \end{gathered}$$

3. Multiply $3x+x^4-2x^2$ by $x^3-2-x$.

Arrange according to the descending powers of $x$. $$\begin{gathered} r*5cr{x}^4\&-\&2x^2\&+\&\mathrm{\backslash PadTo}[l]3x^{4}3x\&\&\&\&\&\& \\ {x}^3\&-\&\mathrm{\backslash PadTo}[c]2x^{2}x\&-\&\mathrm{\backslash PadTo}[l]3x^{4}2\&\&\&\&\&\& \\ \mathrm{\backslash cline}1-5x^7\&-\&2x^5\&+\&3x^4\&\&\&\&\&\& \\ \&-\&x^5\&\&\&+\&2x^3\&-\&3x^2\&\& \\ \&\&\&-\&2x^4\&\&\&+\&4x^2\&-\&6x \\ \mathrm{\backslash hline}{x}^7\&-\&3x^5\&+\&x^4\&+\&2x^3\&+\&x^2\&-\&6x \end{gathered}$$

4. Multiply $a^2+b^2+c^2-ab-bc-ac$ by $a+b+c$.

Arrange according to