phân tích thành nhân tử
`a^7 - a^5 +2a^3 +2a^2`
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
PH
0
15 tháng 7 2021
Ta có: \(b\left(a-5\right)-2a+10\)
\(=b\left(a-5\right)-2\left(a-5\right)\)
\(=\left(a-5\right)\left(b-2\right)\)
22 tháng 7 2023
`a^2 + ab + 2a + 2b = a(a+2) + b(a+2) = (a+b)(a+2)`
NG
1
19 tháng 9 2021
\(a^6-a^4+2a^3+2a^2=a^4\left(a^2-1\right)+2a^2\left(a+1\right)\)
\(=a^4\left(a-1\right)\left(a+1\right)+2a^2\left(a+1\right)=\left(a+1\right)\left(a^5-a^4+2a^2\right)\)
TT
Phân tích đa thức thành nhân tử:
\(\left(4x^2-25\right)^2-9\left(2x-5\right)^2\)
\(a^6-a^4+2a^3+2a^2\)
1
SM
25 tháng 9 2018
a) \(\left(4x^2-25\right)^2-9\left(2x-5\right)^2\)
\(=\left(4x^2-25\right)^2-\left(6x-15\right)^2\)
\(=\left(4x^2-25-6x+15\right)\left(4x^2-25+6x-15\right)\)
\(=\left(4x^2-6x-10\right)\left(4x^2+6x-40\right)\)
\(=\left(4x^2+4x-10x-10\right)\left(4x^2+16x-10x-40\right)\)
\(=\left[4x\left(x+1\right)-10\left(x+1\right)\right]\left[4x\left(x+4\right)-10\left(x+4\right)\right]\)
\(=\left(4x-10\right)\left(x+1\right)\left(4x-10\right)\left(x+4\right)\)
\(=\left(4x-10\right)^2\left(x+1\right)\left(x+4\right)\)
\(=4\left(2x-5\right)^2\left(x+1\right)\left(x+4\right)\)
b) \(a^6-a^4+2a^3+2a^2\)
\(=a^2\left(a^4-a^2+2a+2\right)\)
\(=a^2\left(a^4+a^3-a^3-a^2+2a+2\right)\)
\(=a^2\left[a^3\left(a+1\right)-a^2\left(a+1\right)+2\left(a+1\right)\right]\)
\(=a^2\left(a+1\right)\left(a^3-a^2+2\right)\)
9 tháng 7 2016
\(a^6-a^4+2a^3+2a^2\)
\(=\left[\left(a^3\right)^2-\left(a^2\right)^2\right]+2\left(a^2+a^3\right)\)
\(=\left(a^3-a^2\right)\left(a^3+a^2\right)+2\left(a^3+a^2\right)\)
\(=\left(a^3-a^2+2\right)\left(a^3+a^2\right)\)
\(=a^2.\left(a^3-a^2+2\right)\left(a+1\right)\)
9 tháng 7 2016
\(a^6-a^4+2a^3+2a^2=a^2\left(a^4-a^2+2a+2\right)=a^2\left[a^2\left(a^2-1\right)+2\left(a+1\right)\right]\)
\(=a^2\left[a^2\left(a-1\right)\left(a+1\right)+2\left(a+1\right)\right]=a^2\left(a+1\right)\left(a^3-a^2+2\right)=a^2\left(a+1\right)^2\left(a^2-2a+2\right)\)
HN
2
10 tháng 10 2017
b)\(2a^2-3+5a\)
\(=\left(2a^2+6a\right)-\left(a+3\right)\)
\(=\left(a+3\right)\left(2a-1\right)\)
d)\(2a^2-5-3a\)
\(=\left(2a^2+2a\right)-\left(5a+5\right)\)
\(=\left(a+1\right)\left(2a-5\right)\)
10 tháng 10 2017
a) \(a^2-3-2a\)
\(=a^2-2a+1-4\)
\(=\left(a^2-2a+1\right)-2^2\)
\(=\left(a-1\right)^2-2^2\)
\(=\left(a-1-2\right)\left(a-1+2\right)\)
\(=\left(a-3\right)\left(a+1\right)\)
c) \(4a+a^2+3\)
\(=a^2+4a+4-1\)
\(=\left(a^2+4a+4\right)-1^2\)
\(=\left(a+2\right)^2-1^2\)
\(=\left(a+2-1\right)\left(a+2+1\right)\)
\(=\left(a+1\right)\left(a+3\right)\)
DT
1
13 tháng 8 2015
a) 4(2x-3)^2-9(4x^2-9)^2
=[2(2x-3)]^2-[3(4x^2-9)]^2
=(4x-6)^2-(12x^2-27)^2
=(4x-6+12x^2-27)(4x-6-12x^2+27)
=(12x^2+4x-33)(4x-12x^2+21)
b) a^6-a^4+2a^3+2a^2
=a^4(a^2-1)+2a^2(a+1)
=a^4(a+1)(a-1)+2a^2(a+1)
=(a+1)[(a^4)(a-1)+2a^2]
=(a+1)(a^5+a^4+2a^2)
PV
1
3 tháng 7 2016
cái này mk chưa hok tới!!!
54746746745764565465476467568457879797689685856
\(a^7-a^5+2a^3+2a^2\\ =a^5\left(a^2-1\right)+2a^2\left(a+1\right)\\ =a^5\left(a-1\right)\left(a+1\right)+2a^2\left(a+1\right)\\ =a^2\left(a+1\right)\left(a^4-a^3+2\right)\)
\(a^7-a^5+2a^3+2a^2=a^5\left(a^2-1\right)+2a^2\left(a+1\right)\)
\(=\left(a+1\right)\left[a^5\left(a-1\right)+2a^3\right]\)
\(=a^3\left(a+1\right)\left[a^2\left(a-1\right)+2\right]\)
\(=a^3\left(a+1\right)\left(a^3-a^2-2\right)\)