5. 因式分解:
(1)$x^4 -13x^2 +36$;
(2)$x^2y^2 -5xy -14$;
(3)$(2x+3)^2 +8(2x+3)-9$。
拓展与思考
(1)$x^4 -13x^2 +36$;
(2)$x^2y^2 -5xy -14$;
(3)$(2x+3)^2 +8(2x+3)-9$。
拓展与思考
答案
(1)
$\begin{aligned}x^{4}-13x^{2}+36 \\= (x^{2}-4)(x^{2}-9)\\=(x + 2)(x - 2)(x + 3)(x - 3)\end{aligned}$
(2)
$\begin{aligned}x^{2}y^{2}-5xy - 14\\=(xy - 7)(xy+2)\end{aligned}$
(3)
设2x + 3 = a,则
$\begin{aligned}(2x + 3)^{2}+8(2x + 3)-9\\=a^{2}+8a - 9\\=(a + 9)(a - 1)\\=(2x+3 + 9)(2x+3 - 1)\\=(2x + 12)(2x + 2)\\=4(x + 6)(x + 1)\end{aligned}$
$\begin{aligned}x^{4}-13x^{2}+36 \\= (x^{2}-4)(x^{2}-9)\\=(x + 2)(x - 2)(x + 3)(x - 3)\end{aligned}$
(2)
$\begin{aligned}x^{2}y^{2}-5xy - 14\\=(xy - 7)(xy+2)\end{aligned}$
(3)
设2x + 3 = a,则
$\begin{aligned}(2x + 3)^{2}+8(2x + 3)-9\\=a^{2}+8a - 9\\=(a + 9)(a - 1)\\=(2x+3 + 9)(2x+3 - 1)\\=(2x + 12)(2x + 2)\\=4(x + 6)(x + 1)\end{aligned}$
1. 因式分解:
(1) $2y+3xy=\_\_\_\_\_\_$;
(2) $2(a+2)+3b(a+2)=\_\_\_\_\_\_$;
(3) $2a+4+3ab+6b=\_\_\_\_\_\_$.
(1) $2y+3xy=\_\_\_\_\_\_$;
(2) $2(a+2)+3b(a+2)=\_\_\_\_\_\_$;
(3) $2a+4+3ab+6b=\_\_\_\_\_\_$.
答案
(1)y(2+3x).(2)(a+2)(2+3b).(3)(a+2)(2+3b).
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