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11. 分解因式：$5a(a - 2b)^{3} - 15b(2b - a)^{3} = $
$5(a - 2b)^{3}(a + 3b)$（或写成$5(a + 3b)(a - 2b)^{3}$）
.
答案：
$5(a - 2b)^{3}(a + 3b)$（或写成$5(a + 3b)(a - 2b)^{3}$）
12. 分解因式：$-x^{2}y^{4} + 16y^{2} = $
$-y^{2}(xy + 4)(xy - 4)$
.
答案：
$-y^{2}(xy + 4)(xy - 4)$。
13. 分解因式：$8ax^{2} - 16axy + 8ay^{2} = $
$8a(x - y)^{2}$
.
答案：
$8a(x - y)^{2}$
14. 利用因式分解计算：$167^{2} + 167×66 + 33^{2} = $
40000
.
答案：
40000
15. 已知 $x + y = 5$,$x^{2} + y^{2} = 13$,则 $x^{3}y + 2x^{2}y^{2} + xy^{3}$ 的值等于
150
.
答案：
150
16. 代数式 $5x^{2} - 4xy + y^{2} + 6x + 20$ 的最小值为
11
.
答案：
11
17. (本小题 8 分)
把下列各式因式分解：
(1)$3x - 27x^{3}$；
(2)$m(x - 3)^{2} - 2m(x - 3) + m$；
(3)$(a^{2} + 1)^{2} - 4a^{2}$；
(4)$16(a + b)^{2} - 9(a - b)^{2}$.
把下列各式因式分解：
(1)$3x - 27x^{3}$；
(2)$m(x - 3)^{2} - 2m(x - 3) + m$；
(3)$(a^{2} + 1)^{2} - 4a^{2}$；
(4)$16(a + b)^{2} - 9(a - b)^{2}$.
答案：
(1)
$\begin{aligned}3x - 27x^{3} &= 3x(1 - 9x^{2}) \\&= 3x(1 + 3x)(1 - 3x)\end{aligned}$
(2)
$\begin{aligned}m(x - 3)^{2} - 2m(x - 3) + m &= m[(x - 3)^{2} - 2(x - 3) + 1] \\&= m[(x - 3) - 1]^{2} \\&= m(x - 4)^{2}\end{aligned}$
(3)
$\begin{aligned}(a^{2} + 1)^{2} - 4a^{2} &= (a^{2} + 1 + 2a)(a^{2} + 1 - 2a) \\&= (a + 1)^{2}(a - 1)^{2}\end{aligned}$
(4)
$\begin{aligned}16(a + b)^{2} - 9(a - b)^{2} &= [4(a + b) + 3(a - b)][4(a + b) - 3(a - b)] \\&= (4a + 4b + 3a - 3b)(4a + 4b - 3a + 3b) \\&= (7a + b)(a + 7b)\end{aligned}$
(1)
$\begin{aligned}3x - 27x^{3} &= 3x(1 - 9x^{2}) \\&= 3x(1 + 3x)(1 - 3x)\end{aligned}$
(2)
$\begin{aligned}m(x - 3)^{2} - 2m(x - 3) + m &= m[(x - 3)^{2} - 2(x - 3) + 1] \\&= m[(x - 3) - 1]^{2} \\&= m(x - 4)^{2}\end{aligned}$
(3)
$\begin{aligned}(a^{2} + 1)^{2} - 4a^{2} &= (a^{2} + 1 + 2a)(a^{2} + 1 - 2a) \\&= (a + 1)^{2}(a - 1)^{2}\end{aligned}$
(4)
$\begin{aligned}16(a + b)^{2} - 9(a - b)^{2} &= [4(a + b) + 3(a - b)][4(a + b) - 3(a - b)] \\&= (4a + 4b + 3a - 3b)(4a + 4b - 3a + 3b) \\&= (7a + b)(a + 7b)\end{aligned}$
18. (本小题 8 分)
分解因式：
(1)$9a^{2}(x - y) + 4b^{2}(y - x)$；
(2)$(m + n)^{2} - 2(m^{2} - n^{2}) + (m - n)^{2}$；
(3)$9x^{2} - 4 - (x + 1)(3x + 2)$；
(4)$x^{4} - 16y^{4}$.
分解因式：
(1)$9a^{2}(x - y) + 4b^{2}(y - x)$；
(2)$(m + n)^{2} - 2(m^{2} - n^{2}) + (m - n)^{2}$；
(3)$9x^{2} - 4 - (x + 1)(3x + 2)$；
(4)$x^{4} - 16y^{4}$.
答案：
(1)
$\begin{aligned}&9a^{2}(x - y) + 4b^{2}(y - x)\\=&9a^{2}(x - y)-4b^{2}(x - y)\\=&(x - y)(9a^{2}-4b^{2})\\=&(x - y)(3a + 2b)(3a - 2b)\end{aligned}$
(2)
$\begin{aligned}&(m + n)^{2}-2(m^{2}-n^{2})+(m - n)^{2}\\=&(m + n)^{2}-2(m + n)(m - n)+(m - n)^{2}\\=&[(m + n)-(m - n)]^{2}\\=&(m + n - m + n)^{2}\\=&(2n)^{2}\\=&4n^{2}\end{aligned}$
(3)
$\begin{aligned}&9x^{2}-4-(x + 1)(3x + 2)\\=&9x^{2}-4-(3x^{2}+2x+3x + 2)\\=&9x^{2}-4 - 3x^{2}-5x - 2\\=&(9x^{2}-3x^{2})-5x-(4 + 2)\\=&6x^{2}-5x - 6\\=&(2x - 3)(3x + 2)\end{aligned}$
(4)
$\begin{aligned}&x^{4}-16y^{4}\\=&(x^{2})^{2}-(4y^{2})^{2}\\=&(x^{2}+4y^{2})(x^{2}-4y^{2})\\=&(x^{2}+4y^{2})(x + 2y)(x - 2y)\end{aligned}$
(1)
$\begin{aligned}&9a^{2}(x - y) + 4b^{2}(y - x)\\=&9a^{2}(x - y)-4b^{2}(x - y)\\=&(x - y)(9a^{2}-4b^{2})\\=&(x - y)(3a + 2b)(3a - 2b)\end{aligned}$
(2)
$\begin{aligned}&(m + n)^{2}-2(m^{2}-n^{2})+(m - n)^{2}\\=&(m + n)^{2}-2(m + n)(m - n)+(m - n)^{2}\\=&[(m + n)-(m - n)]^{2}\\=&(m + n - m + n)^{2}\\=&(2n)^{2}\\=&4n^{2}\end{aligned}$
(3)
$\begin{aligned}&9x^{2}-4-(x + 1)(3x + 2)\\=&9x^{2}-4-(3x^{2}+2x+3x + 2)\\=&9x^{2}-4 - 3x^{2}-5x - 2\\=&(9x^{2}-3x^{2})-5x-(4 + 2)\\=&6x^{2}-5x - 6\\=&(2x - 3)(3x + 2)\end{aligned}$
(4)
$\begin{aligned}&x^{4}-16y^{4}\\=&(x^{2})^{2}-(4y^{2})^{2}\\=&(x^{2}+4y^{2})(x^{2}-4y^{2})\\=&(x^{2}+4y^{2})(x + 2y)(x - 2y)\end{aligned}$
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