phân tích đa thức thành nhân tử:
\(\left(x^2-3\right)^2+16\)
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HK
1
28 tháng 8 2017
Ta có
(x2-3)2+16
=x4-6x2+9+16
=x4-6x2+25
=x4+10x2+25-16x2
=(x2+5)2-16x2
=(x2+5-4x)(x2+5+4x)
14 tháng 8 2021
1: \(6x^2y-9xy^2+3xy\)
\(=3xy\left(2x-3y+1\right)\)
2: \(\left(4-x\right)^2-16\)
\(=\left(4-x-4\right)\left(4-x+4\right)\)
\(=-x\cdot\left(8-x\right)\)
3: \(x^3+9x^2-4x-36\)
\(=x^2\left(x+9\right)-4\left(x+9\right)\)
\(=\left(x+9\right)\left(x-2\right)\left(x+2\right)\)
14 tháng 8 2021
1) \(6x^2y-9xy^2+3xy=3xy\left(2x-3y+1\right)\)
2) \(\left(4-x\right)^2-16=\left(4-x\right)^2-4^2=\left(4-x-4\right)\left(4-x+4\right)=-x\left(8-x\right)\)
3) \(x^3+9x^2-4x-36\\ =\left(x^3-2x^2\right)+\left(11x^2-22x\right)+\left(18x-36\right)\\ =x^2\left(x-2\right)+11x\left(x-2\right)+18\left(x-2\right)\\ =\left(x^2+11x+18\right)\left(x-2\right)\\ =\left[\left(x^2+2x\right)+\left(9x+18\right)\right]\left(x-2\right)\\ =\left[x\left(x+2\right)+9\left(x+2\right)\right]\left(x-2\right)\\ =\left(x+2\right)\left(x+9\right)\left(x-2\right)\)
2 tháng 8 2016
\(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+16\)
\(=\left(x+2\right)\left(x+8\right)\left(x+4\right)\left(x+6\right)+16\)
\(=\left(x^2+8x+2x+16\right)\left(x^2+6x+4x+24\right)+16\)
\(=\left(x^2+10x+16\right)\left(x^2+10x+24\right)+16\)
\(=\left(x^2+10x+16\right)\left(x^2+10+16+8\right)+16\)
\(=\left(x^2+10x+16\right)^2+2.\left(x^2+10x+16\right).4+4^2\)
\(=\left(x^2+10x+16+4\right)^2\)
\(=\left(x^2+10+20\right)^2\)
2 tháng 8 2016
\(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+16\)
\(=\left[\left(x+2\right)\left(x+8\right)\right]\left[\left(x+4\right)\left(x+6\right)\right]+16\)
\(=\left(x^2+8x+2x+16\right)
\left(x^2+6x+4x+24\right)+16\)
\(=\left(x^2+10x+16\right)\left(x^2+10x+24\right)+16\left(1\right)\)
\(\text{Đặt }x^2+10x+\frac{16+24}{2}=t\)
\(\text{hay }x^2+10x+20=t\)
\(\left(1\right)\Rightarrow\left(t-4\right)\left(t+4\right)+16\)
\(=t^2-4^2+16\)
\(=t^2-16+16\)
\(=t^2\)
\(=\left(x^2+10x+20\right)^2\)
24 tháng 9 2019
\(\left(x-2\right)\left(x-4\right)\left(x-6\right)\left(x-8\right)+16\)
\(=\left[\left(x-2\right)\left(x-8\right)\right]\left[\left(x-4\right)\left(x-6\right)\right]+16\)
\(=\left(x^2-10x+16\right)\left(x^2-10x+24\right)+16\)(1)
Đặt \(x^2-10x+20=t\)thay vào (1) ta được :
\(\left(t-4\right)\left(t+4\right)+16\)
\(=t^2-16+16\)
\(=t^2\)Thay \(t=x^2-10x+20\)ta được :
\(\left(x^2-10x+20\right)^2\)
\(=\left(x^2-2.5.x+25-25+20\right)^2\)
\(=\left[\left(x-5\right)^2-5\right]^2\)
\(=\left(x-5-\sqrt{5}\right)^2\left(x-5+\sqrt{5}\right)^2\)
7 tháng 10 2018
\(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+16\)
\(=\left[\left(x+2\right)\left(x+8\right)\right]\left[\left(x+4\right)\left(x+6\right)\right]+18\)
\(=\left(x^2+10x+16\right)\left(x^2+10x+24\right)+16\)
\(=\left(x^2+10x+20-4\right)\left(x^2+10x+20+4\right)-16\)
\(=\left(x^2+10x+20\right)^2-16+16=\left(x^2+10x+20\right)^2\)
Chúc bạn học tốt.
23 tháng 10 2019
\(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+16\)
\(\Rightarrow\left[\left(x+2\right)\left(x+8\right)\right]\left[\left(x+6\right)\left(x+8\right)\right]+16\)
\(\Rightarrow\left(x^2+10x+16\right)\left(x^2+10x+24\right)+16\)
\(\Rightarrow\left(x^2+10x+16\right)\left[\left(x^2+10x+16\right)+8\right]+16\)
\(\Rightarrow\left(x^2+10x+16\right)^2+8\left(x^2+10x+16\right)+4^2\)
\(\Rightarrow\left(x^2+10x+20\right)^2\)
L
2
2 tháng 10 2016
25(x-y)2-16(x+y)2
=[5(x-y)]2-[4(x+y)]2
=[5x-5y]2-[4x+4y]2
=(5x-5y+4x+4y)[(5x-5y)-(4x+4y)]
=(9x-y)(x-9y)
K
4
R
6 tháng 1 2022
x3+27+(x+3)(x+9)
= (x+3)(x2-3x+9)+(x+3)(x+9)
= (x+3)(x2-3x+9+x+9)
=(x+3)(x2-2x+18)
6 tháng 1 2022
\(=\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)\\ =\left(x+3\right)\left(x^2-3x+9+x-9\right)\\ =\left(x+3\right)\left(x^2-2x\right)=x\left(x-2\right)\left(x+3\right)\)
NQ
2
TA
10 tháng 7 2021
`(x+3)^4+(x+5)^4-2`
`={[(x+3)^2]^2-1^2}+{[(x+5)^2]^2 -1^2}`
`=[(x+3)^2-1^2][(x+3)^2+1]+[(x+5)^2-1^2][(x+5)^2+1]`
`=(x+3-1)(x+3+1)[(x+3)^2+1]+(x+5-1)(x+5+1)[(x+5)^2+1]`
`=(x+2)(x+4)[(x+3)^2+1]+(x+4)(x+6)[(x+5)^2+1]`
`=(x+4){(x+2)[(x+3)^2+1]+(x+6)[(x+5)^2+1]}`
`=(x+4)(2x^3+24x^2+108x+176)`
10 tháng 7 2021
Bạn gì ơi hình như phải ra \(2\left(t+4\right)^2\left(x^2+8x+22\right)\)chứ nhỉ???
NT
2
KN
18 tháng 7 2019
\(x^2-16+2\left(x+4\right)\)
\(=\left(x+4\right)\left(x-4\right)+2\left(x+4\right)\)
\(=\left(x+4\right)\left(x-4+2\right)\)
\(=\left(x+4\right)\left(x-2\right)\)
addws