题目
[题目]因式分解-|||-(1) 4a(x-3)+2b(3-x)-|||-(2) ^4-18(x)^2+81-|||-(3) ((1-b))^3+2((b-1))^2
题目解答
答案
解析
步骤 1：提取公因式
(1) 4a(x-3)+2b(3-x) = 4a(x-3)-2b(x-3) = 2(x-3)(2a-b)
步骤 2：完全平方公式
(2) ${x}^{4}-18{x}^{2}+81$ = ${({x}^{2}-9)}^{2}$ = ${(x+3)}^{2}{(x-3)}^{2}$
步骤 3：提取公因式
(3) $4b{(1-b)}^{3}+2{(b-1)}^{2}$ = $4b{(1-b)}^{3}+2{(1-b)}^{2}$ = $2{(1-b)}^{2}(2b-2{b}^{2}+1)$
(1) 4a(x-3)+2b(3-x) = 4a(x-3)-2b(x-3) = 2(x-3)(2a-b)
步骤 2：完全平方公式
(2) ${x}^{4}-18{x}^{2}+81$ = ${({x}^{2}-9)}^{2}$ = ${(x+3)}^{2}{(x-3)}^{2}$
步骤 3：提取公因式
(3) $4b{(1-b)}^{3}+2{(b-1)}^{2}$ = $4b{(1-b)}^{3}+2{(1-b)}^{2}$ = $2{(1-b)}^{2}(2b-2{b}^{2}+1)$