Phân tích thành nhân tử :
a, \(x^4+4\)
b, \(4x^8+1\)
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YH
1
MT
20 tháng 8 2015
a. x^2 -2x -8
=x2+2x-4x-8
=x.(x+2)-4.(x-2)
=(x+2)(x-4)
b. 4x^4 - 4x -35
=4x2+10x-14x-35
=2x.(2x+5)-7.(2x+5)
=(2x+5)(2x-7)
TM
28 tháng 6 2017
a)\(7x\left(y-4\right)^2-\left(4-y\right)^3=7x\left(4-y\right)^2-\left(4-y\right)^3=\left(4-y\right)^2\left(7x-4+y\right)\)
b)\(\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)+9\left(8-4x\right)\)
\(=\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)-9\left(4x-8\right)\)
\(=\left(4x-8\right)\left(x^2-x-10\right)=4\left(x-2\right)\left(x^2-x-10\right)\)
28 tháng 6 2017
a.\(7x.\left(y-4\right)^2-\left(4-y\right)^3\)=\(7x.\left(4-y\right)^2-\left(4-y\right)^3=\left(4-y\right)^2.\left(7x+y-4\right)\)
b.\(\left(4x-8\right).\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)+9.\left(8-4x\right)\)
=\(\left(4x-8\right)\left(x^2+6-x-7-9\right)=\left(4x-8\right)\left(x^2-x-10\right)\)
NH
13 tháng 11 2019
1, a4 + a2 + 1
= a4 + 2a2 + 1 - a2
= (a2)2 + 2a2 + 1 - a2
= (a2 + 1)2 - a2
= (a2 + 1 - a)(a2 + 1 + a)
2, a4 + 4b4
= (a2)2 + 2. a2 . b2 + (2b)2 - a2 . b2
= (a2 + 2b)2 - (ab)2
= (a2 + 2b - ab)(a2 + 2b + ab)
3, 64x4 + 1
= (8x2)2 + 16x2 + 1 - 16x2
= (8x2 + 1)2 - (4x)2
= (8x2 + 1 - 4x)(8x2 + 1 + 4x)
4, x5 + x4 + 1
= x5 + x4 + x3 - x3 - x2 - x + x + x2 + 1
= (x5 + x4 + x3) - (x3 + x2 + x) + (x + x2 + 1)
= x3(x2 + x + 1) - x(x2 + x + 1) + (x2 + x + 1)
= (x2 + x + 1)(x3 - x + 1)
5, x7 + x2 + 1
= x7 – x + x2 + x + 1
= x(x6 – 1) + (x2 + x + 1)
= x(x3 – 1)(x3 + 1) + (x2 + x + 1)
= x(x3 + 1)(x – 1) (x2 + x + 1) + (x2 + x + 1)
= (x2 + x + 1)[ x(x3 + 1)(x – 1) + 1]
= (x2 + x + 1)(x5 – x4 + x3 – x2 + x – 1)
6, x8 + x + 1
= x8 + x7 + x6 - x7 - x6 - x5 + x5 + x4 + x3 - x4 - x3 - x2 + x2 + x + 1
= (x8 + x7 + x6) - (x7 + x6 + x5) + (x5 + x4 + x3 ) - (x4 + x3 + x2) + (x2 + x + 1)
= x6(x2 + x + 1) - x5(x2 + x + 1) + x3(x2 + x + 1) - x2(x2 + x + 1) + (x2 + x + 1)
= (x2 + x + 1)(x6 - x5 + x3 - x2 + 1)
7, x4 - 4x2 + 4x - 1
= x4 - (4x2 - 4x + 1)
= (x2)2 - (2x - 1)2
= (x2 - 2x + 1)(x2 + 2x - 1)
= (x - 1)2 (x2 + 2x - 1)
8, a16 + a8b8 + b16
= (a16 + 2a8b8 + b16) - a8b8
= (a8 + b8)2 - (a4b4)2
= (a8 + b8 - a4b4)(a8 + b8 + a4b4)
= (a8 + b8 - a4b4)[(a8 + b8 + 2a4b4) - a4b4]
= (a8 + b8 - a4b4)[(a4 + b4)2 - (a2b2)2]
= (a8 + b8 - a4b4)(a4 + b4 - a2b2)(a4 + b4 + a2b2)
= (a8 + b8 - a4b4)(a4 + b4 - a2b2)[(a4 + b4 + 2a2b2) - a2b2]
= (a8 + b8 - a4b4)(a4 + b4 - a2b2)[(a2 + b2) - (ab)2]
= (a8 + b8 - a4b4)(a4 + b4 - a2b2)(a2 + b2 - ab)(a2 + b2 + ab)
L
15 tháng 11 2019
1)
=a^4+2a^2+1-a^2
=(a^2+1)^2-a^2
=(a^2-a+1)(a^2+a+1)
2)
=a^4+4b^4-4a^2b^2
=(a^2+2b^2)^2-4a^2b^2
=(a^2-2ab+2b^2)(a^2+2ab+2b^2)
3)
=(8x^2+1)^2-16x^2
=(8x^2-4x+1)(8x^2+4x+1).
4)
=x^5+x^4+x^3-x^3+1
=x^2(x^2+x+1)-(x-1)(x^2+x+1)
=(x^2-x+1)(x^2+x+1)
5).
=x^7-x+x^2+x+1
=x(x^6-1)+x^2+x+1
=x(x^3-1)(x^3+1)+x^2+x+1
=x(x-1)(x^2+x+1)(x^3+1)+x^2+x+1
=(x^2+x+1)[(x^2-x)(x^3+1)+1]
6)
=x^8-x^2+x^2+x+1
=x^2(x-1)(x^2+x+1)(x^3+1)+x^2+x+1
Xong nhóm x^2+x+1 vào.
7)
=x^4-(2x-1)^2
=(x^2-2x+1)(x^2+2x-1)
8)
=(a^8+b^8)^2-a^8b^8
=(a^8-a^4b^4+b^8)(a^8+a^4b^4+b^8).
BK
1
MT
5 tháng 8 2015
4x4-37x2+9
=4x4-12x2+9-25
=(2x2-3)2-25
=(2x2-3-5)(2x2-3+5)
=(2x2-8)(2x2+2)
=2.(x2-4).2.(x2+1)
=4(x-2)(x+2)(x2+1)
x^8+x^4+1
=x8+2x4+1-x4
=(x4+1)2-x4
=(x4-x2+1)(x4+x2+1)
=(x4-x2+1)(x4+2x2+1-x2)
=(x4-x2+1)[(x2+1)2-x2]
=(x4-x2+1)(x2-x+1)(x2+x+1)
a) \(\Rightarrow\left(x^2\right)^2+\left(2^2\right)^2+2.2x^2-2.2x^2\Rightarrow\left(x^2+2\right)^2-\left(2x\right)^2\Rightarrow\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)
b) \(\Rightarrow\left(2x^4\right)^2+2.2.x^4.1+1-2.2.x^4.1\Rightarrow\left(2x^4+1\right)^2-\left(2x^2\right)^2\Rightarrow\left(2x^4+1-2x^2\right)\left(2x^4+1+2x^2\right)\)
CHÚC BẠN học tốt
T I C K cho mình nha cảm ơn
\(x^4+4\)
\(=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-4x^2\)
\(=\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)