Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$Q(x)-x^{3}+px^{2}+9x+6; x^{3}+px^{2}\times qx+5$$

Answer

$$Q*x-x^3+p*x^2+9*x+6;x^3+p*x^3*q+5$$

Solution


Regroup terms.
\[\begin{aligned}&Qx-{x}^{3}+p{x}^{2}+9x+6\\&{x}^{3}+p{x}^{2}xq+5\end{aligned}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\begin{aligned}&Qx-{x}^{3}+p{x}^{2}+9x+6\\&{x}^{3}+p{x}^{2+1}q+5\end{aligned}\]
Simplify  \(2+1\)  to  \(3\).
\[\begin{aligned}&Qx-{x}^{3}+p{x}^{2}+9x+6\\&{x}^{3}+p{x}^{3}q+5\end{aligned}\]
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