32013中３・多項式の因数分解・計算問題・分配法則3

(1) $\begin{array}{r}2x^3-x^2{y}^2+3x^{2}y\end{array}$

$\begin{array}{rcl}& =& x^2\times 2x+x^2\times (-y^2)+x^2\times 3y\\ & =& x^2(2x-y^2+3y)\end{array}$

答$x^2(2x-y^2+3y)$

(2) $\begin{array}{r}4a^3{b}^2-8a^{3}b+12a^2{b}^2\end{array}$

$\begin{array}{rcl}& =& 4a^{2}b\times ab+4a^{2}b\times (-2a)+4a^{2}b\times 3b\\ & =& 4a^{2}b(ab-2a+3b)\end{array}$

答$4a^{2}b(ab-2a+3b)$