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a^4(b - c) + b^4(c - a) + c^4(a - b)
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LV
1
6 tháng 12 2021
\(a,=4x^3\left(x+1\right)-x\left(x+1\right)=x\left(4x^2-1\right)\left(x+1\right)\\ =x\left(2x-1\right)\left(2x+1\right)\left(x+1\right)\\ b,=\left(a-1\right)^2-\left(b-c\right)^2\\ =\left(a-1-b+c\right)\left(a-1+b-c\right)\\ c,=\left(x^2-9x+14\right)\left(x^2-9x+20\right)-72\\ =\left(x^2-9x+17\right)^2-9-72\\ =\left(x^2-9x+17\right)^2-81=\left(x^2-9x+8\right)\left(x^2-9x+26\right)\\ =\left(x-1\right)\left(x-8\right)\left(x^2-9x+26\right)\)
17 tháng 10 2021
Bài 1:
a: \(49-4x^2=\left(7-2x\right)\left(7+2x\right)\)
b: \(x^3+8=\left(x+2\right)\left(x^2-2x+4\right)\)
c: \(x^2+18xy+81y^2=\left(x+9y\right)^2\)
MN
1
NV
Nguyễn Việt Lâm
Giáo viên
3 tháng 1
a.
\(x^4+4=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-\left(2x\right)^2=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)
b.
\(x^3-9x^2+6x+16=\left(x^3-7x^2-8x\right)-\left(2x^2-14x-16\right)\)
\(=x\left(x^2-7x-8\right)-2\left(x^2-7x-8\right)\)
\(=\left(x-2\right)\left(x^2-7x-8\right)=\left(x-2\right)\left(x^2+x-8x-8\right)\)
\(=\left(x-2\right)\left[x\left(x+1\right)-8\left(x+1\right)\right]=\left(x-2\right)\left(x+1\right)\left(x-8\right)\)
c.
\(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
\(=\left(x+2\right)\left(x+5\right)\left(x+3\right)\left(x+4\right)-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+10+2\right)-24\)
\(=\left(x^2+7x+10\right)^2+2\left(x^2+7x+10\right)-24\)
\(=\left(x^2+7x+10\right)^2-4\left(x^2+7x+10\right)+6\left(x^2+7x+10\right)-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+10-4\right)+6\left(x^2+7x+10-4\right)\)
\(=\left(x^2+7x+10-4\right)\left(x^2+7x+10+6\right)=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)
\(=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)
LV
1
LV
1
DT
1
HN
22 tháng 8 2021
\(a^4\left(b-c\right)+b^4\left(c-a\right)+c^4\left(a-b\right)\)
\(=a^4\left(a+b-a-c\right)+b^4\left(c-a\right)+c^4\left(a-b\right)\)
\(=-a^4\left(c-a\right)-a^4\left(a-b\right)+b^4\left(c-a\right)+c^4\left(a-b\right)\)
\(=\left(b^4-a^4\right)\left(c-a\right)+\left(c^4-a^4\right)\left(a-b\right)\)
\(=\left(b^2+a^2\right)\left(b^2-a^2\right)\left(c-a\right)+\left(c^2-a^2\right)\left(c^2+a^2\right)\left(a-b\right)\)
\(=\left(b^2+a^2\right)\left(b-a\right)\left(b+a\right)\left(c-a\right)+\left(c-a\right)\left(c+a\right)+\left(c^2+a^2\right)\left(a-b\right)\)
\(=\left(b-a\right)\left(c-a\right)[\left(b^2+a^2\right)\left(a+b\right)-\left(c+a\right)\left(c^2+a^2\right)]\)
\(=\left(b-a\right)\left(c-a\right)\left(ab^2+a^3+b^3+a^2b-c^3-ac^2-a^3-a^2c\right)\)
\(=\left(b-a\right)\left(c-a\right)\left(ab^2+b^3+a^2b-c^3-ac^2-a^2c\right)\)
\(=\left(b-a\right)\left(c-a\right)[\left(ab^2-ac^2\right)+\left(a^2b-a^2c\right)+\left(b^3+c^3\right)]\)
\(=\left(b-a\right)\left(c-a\right)[a\left(b^2-c^2\right)+a^2\left(b-c\right)+\left(b-c\right)\left(b^2+bc+c^2\right)]\)
\(=\left(b-a\right)\left(c-a\right)\left(b-c\right)\left(ab+ac+a^2+b^2+c^2+bc\right)\)
LV
1
(a-b) (c-a) (c-b) (c2+b c+a c+b2+a b+a2)