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a^4(b-c)+b^4(c-a)+c^4(a-b)
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LV
1
TN
23 tháng 8 2023
A=8abc+4(ab+bc+ca)+2(a+b+c)+1�=8���+4(��+��+��)+2(�+�+�)+1
A = 8abc + 4ab + 4bc + 4ca + 2a + 2b + 2c + 1
A=(8abc+4ab)+(4bc+2b)+(4ca+2a)+(2c+1)�=(8���+4��)+(4��+2�)+(4��+2�)+(2�+1)
A=4ab(2c+1)+2b(2c+1)+2a(2c+1)+(2c+1)�=4��(2�+1)+2�(2�+1)+2�(2�+1)+(2�+1)
A=(2c+1)(4ab+2a+2b+1)�=(2�+1)(4��+2�+2�+1)
A=(2c+1)[2a(2b+1)+(2b+1)]�=(2�+1)[2�(2�+1)+(2�+1)]
A=(2a+1)(2b+1)(2c+1)
6 tháng 12 2021
\(a,=4x^3\left(x+1\right)-x\left(x+1\right)=x\left(4x^2-1\right)\left(x+1\right)\\ =x\left(2x-1\right)\left(2x+1\right)\left(x+1\right)\\ b,=\left(a-1\right)^2-\left(b-c\right)^2\\ =\left(a-1-b+c\right)\left(a-1+b-c\right)\\ c,=\left(x^2-9x+14\right)\left(x^2-9x+20\right)-72\\ =\left(x^2-9x+17\right)^2-9-72\\ =\left(x^2-9x+17\right)^2-81=\left(x^2-9x+8\right)\left(x^2-9x+26\right)\\ =\left(x-1\right)\left(x-8\right)\left(x^2-9x+26\right)\)
MN
1
NV
Nguyễn Việt Lâm
Giáo viên
3 tháng 1 2024
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
LV
1
N
1
11 tháng 8 2023
b: =x^3+2x^2-x^2+4
=x^2(x+2)-(x+2)(x-2)
=(x+2)(x^2-x+2)
c: =x^3-2x^2+x^2-4
=x^2(x-2)+(x-2)(x+2)
=(x-2)(x^2+x+2)
d: =(x-y)(x+y)-7(x+y)
=(x+y)(x-y-7)
GH
27 tháng 7 2023
a Đề sai: )
b
\(a^3-a^2x-ay+xy\\ =a^2\left(a-x\right)-y\left(a-x\right)\\ =\left(a-x\right)\left(a^2-y\right)\)
c
\(4x^2-y^2+4x+1\\ =\left(2x\right)^2+2.2x.1+1-y^2\\ =\left(2x+1\right)^2-y^2\\ =\left(2x+1-y\right)\left(2x+1+y\right)\)
d
\(x^4+2x^3+x^2\\ =x^4+x^3+x^3+x^2\\ =x^3\left(x+1\right)+x^2\left(x+1\right)\\ =\left(x^3+x^2\right)\left(x+1\right)\)
e
\(5x^2-10xy+5y^2-5z^2\\ =5\left(x^2-2xy+y^2-z^2\right)\\ =5\left[\left(x-y\right)^2-z^2\right]\\ =5\left(x-y-z\right)\left(x-y+z\right)\)
27 tháng 7 2023
c: =(2x+1)^2-y^2
=(2x+1+y)(2x+1-y)
d: =x^2(x^2+2x+1)
=x^2(x+1)^2
e: =5(x^2-2xy+y^2-z^2)
=5[(x-y)^2-z^2]
=5(x-y-z)(x-y+z)
đơn giản wá
\(a^4\left(b-c\right)+b^4\left(c-a\right)+c^4\left(a-b\right)\)
\(\Leftrightarrow\text{=a^4(b-c)-b^4[(b-c)+(a-b)]+c^4(a-b) =(b-c)(a^4-b^4)+(a-b)(c^4-b^4)}\)
\(\text{=(b-c)(a^2-b^2)(a^2+b^2)+(a-b)(c^2-b^2)... =(b-c)(a-b)(a+b)(a^2+b^2)-(a-b)(b-c)(b+... }\)
\(\text{=(b-c)(a-b)(a^3+ab^2+ba^2+b^3-bc^2-b^3-... mà ta có a^3+ab^2+ba^2-bc^2-c^3-cb^2 }\)
\(\text{=(a^3-c^3)+b^2(a-c)+b(a^2-c^2) =(a-c)(a^2+ac+c^2)+b^2(a-c)+b(a-c)(a+c) }\)
\(\text{=(a-c)(a^2+ac+c^2+b^2+ab+ac) } \)
\(\text{từ đó suy ra a^4(b-c)+b^4(c-a)+c^4(a-b) =(a-b)(b-c)(c-a)(a^2+b^2+c^2+ab+bc+ca)}\)