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`k) 81x^4 + 4
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6 tháng 2 2022
\(=81x^2-\left(z+3y\right)^2\)
\(=\left(9x+z+3y\right)\left(9x-z-3y\right)\)
10 tháng 7 2017
1, \(x^3+8x^2+17x+10=\left(x^3+x^2\right)+\left(7x^2+7x\right)+\left(10x+10\right)\)
\(=x^2\left(x+1\right)+7x\left(x+1\right)+10\left(x+1\right)\)\(=\left(x+1\right)\left(x^2+7x+10\right)=\left(x+1\right)\left(x+2\right)\left(x+5\right)\)
2. \(2x^3-3x^2+3x-1=\left(2x^3-x^2\right)-\left(2x^2-x\right)+\left(2x-1\right)\)
\(=x^2\left(2x-1\right)-x\left(2x-1\right)+\left(2x-1\right)\)
\(=\left(2x-1\right)\left(x^2-x+1\right)\)
3. \(x^4+x^2+1=\left(x^4+1\right)+x^2=\left(x^2+1\right)^2-2x^2+x^2\)\(=\left(x^2+1\right)^2-x^2=\left(x^2+x+1\right)\left(x^2-x+1\right)\)
4. \(81x^4+4=\left(9x^2\right)^2+2^2=\left(9x^2+2\right)^2-2.9x^2.2=\left(9x^2+2\right)^2-\left(6x\right)^2\)
\(=\left(9x^2+6x+2\right)\left(9x^2-6x+2\right)\)
Y
17 tháng 6 2019
a) \(A=\left(x^2+x-2\right)\left(x+7\right)-16\)
\(=x^3+8x^2+5x-14-16\)
\(=x^3+8x^2+5x-30\)
\(=x^3+3x^2+5x^2+15x-10x-30\)
\(=x^2\left(x+3\right)+5x\left(x+3\right)-10\left(x+3\right)\)
\(=\left(x^2+5x-10\right)\left(x+3\right)\)
b) \(A=x^4-2x^3-3x^2+4x+4+x^2-4x+4\)
\(=x^4-2x^3-2x^2+8\)
\(=x^3\left(x-2\right)-2\left(x^2-4\right)\)
\(=\left(x-2\right)\left(x^3-2x-4\right)\)
\(=\left(x-2\right)\left[x^2\left(x+2\right)+2x\left(x+2\right)-2\left(x+2\right)\right]\)
\(=\left(x-2\right)\left(x+2\right)\left(x^2+2x-2\right)\)
c) \(81x^4+4=81x^4+36x^2+4-36x^2\)
\(=\left(9x^2+2\right)^2-\left(6x\right)^2\)
\(=\left(9x^2-6x+2\right)\left(9x^2+6x+2\right)\)
d) \(\left(x^2-3\right)^2+16=x^4-6x^2+25\)
\(=\left(x^4+10x^2+25\right)-16x^2\)
\(=\left(x^2+5\right)^2-\left(4x\right)^2\)
\(=\left(x^2-4x+5\right)\left(x^2+4x+5\right)\)
16 tháng 3 2020
\(64x^4+y^4\)
\(=\left(8x^2\right)^2+16x^2y^2+y^4-16x^2y^2\)
\(=\left(8x^2+y^2\right)^2-\left(4xy\right)^2\)
\(=\left(8x^2-4xy+y^2\right)\left(8x^2+4xy+y^2\right)\)
7 tháng 10 2021
\(-\left(x+2\right)+3\left(x^2-4\right)\)
\(=3\left(x-2\right)\left(x+2\right)-\left(x+2\right)\)
\(=\left(x+2\right)\left[3\left(x-2\right)-1\right]=\left(x+2\right)\left(3x-7\right)\)
LK
15 tháng 10 2018
x4 + 1024 = x4 + 64x2 + 1024 - 64x2
= (x2 + 32)2 - (8x)2
= (x2 - 8x + 32)(x2 + 8x + 32)
HY
1
22 tháng 5 2020
Ta có: \(x^4+64\)
\(=\left(x^2\right)^2+2\cdot x^2\cdot8+64-2\cdot x^2\cdot8\)
\(=\left(x^2+8\right)^2-16x^2\)
\(=\left(x^2-4x+8\right)\left(x^2+4x+8\right)\)
\(81x^4+4=81x^4+36x^2+4-36x^2=\left(9x^2+2-6x\right)\left(9x^2+2+6x\right)\)