\(P=a^8+a^4b^4+b^8\)

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21 tháng 3 2019

\(P=\left(a^8+2a^4b^4+b^8\right)-a^4b^4\)

\(P=\left(a^4+b^4\right)^2-a^4b^4\)

\(P=\left(a^4+b^4+a^2b^2\right)\left(a^4+b^4-a^2b^2\right)\)

\(P=\left[\left(a^2+b^2\right)^2-a^2b^2\right]\left(a^4+b^4-a^2b^2\right)\)

\(P=\left(a^2+b^2+ab\right)\left(a^2+b^2-ab\right)\left(a^4+b^4-a^2b^2\right)\)

\(P=\left[\left(a+b\right)^2-ab\right]\left(a^2+b^2-ab\right)\left(a^4+b^4-a^2b^2\right)\)

\(P=\left(a+b+\sqrt{ab}\right)\left(a+b-\sqrt{ab}\right)\left(a^2+b^2-ab\right)\left(a^4+b^4-a^2b^2\right)\)

13 tháng 6 2016

\(a^4+4a^2b^2+4b^4-\left(2ab\right)^2\)

\(=\left(a^2+2b^2\right)^2-\left(2ab\right)^2\)

\(=\left(a^2-2ab+2b^2\right)\left(a^2+2ab+2b^2\right)\)

13 tháng 6 2016

\(x^2-6x+3=x^2-3x-3x+3\)

\(=x\left(x-3\right)-3\left(x-1\right)\)

Ko phân tích được

Tất cả đều ko phân tích được bạn troll mik

Ta có : \(x^8+14x^4+1\)

\(=x^8+2.x^4.7+1\)

\(=x^8+2.x^4.7+49-48\)

\(=\left(x^4+7\right)^2-48\)

\(=\left(x^4+7-\sqrt{48}\right)\left(x^4+7+\sqrt{48}\right)\)

3 tháng 6 2018

a/\(=\left(x^4+1\right)^2+12x^4=\left(x^4+1\right)^2+4x^2\left(x^4+1\right)+4x^4-4x^2\left(x^4+1\right)+8x^4\)

\(=\left(x^4+1+2x^2\right)^2-4x^2\left(x^4+1-2x^2\right)=\left(x^4+2x^2+1\right)-\left(2x^3-2x\right)^2\)

\(=\left(x^4+2x^3+2x^2-2x+1\right)\left(x^4-2x^3+2x^2+2x+1\right)\)

b/\(=\left(x^4+1\right)^2+96x^4=\left(x^4+1\right)^2+16x^2\left(x^4+1\right)+64x^4-16x^2\left(x^4+1\right)+32x^4\)

\(=\left(x^4+1+8x^2\right)^2-16x^2\left(x^4+1-2x^2\right)=\left(x^4+8x^2+1\right)-\left(4x^3-4x\right)^2\)

\(=\left(x^4+4x^3+8x^2-4x+1\right)\left(x^4-4x^3+8x^2+4x+1\right)\)

4 tháng 7 2016

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

\(x^4+4\)

\(=x^4+4x^2+4-4x^2\)

\(=\left(x^2+2\right)^2-4x^2\)

\(=\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)

19 tháng 7 2019

\(A=b^4-9a^2-4b^2+4=b^4-4b^2+4-9a^2\)

\(=\left(b^2-2\right)^2-9a^2\)

\(=\left(b^2-2+3a\right)\left(b^2-2-3a\right)\)

\(A=b^4-9a^2-4b^2+4\)

\(A=\left(b^2\right)^2-2.2.b^2+2^2-9a^2\)

\(A=\left(b^2-2\right)^2-\left(3a\right)^2\)

\(A=\left(b^2-2-3a\right)\left(b^2-2+3a\right)\)

_Hắc phong_

26 tháng 7 2019

\(A=x^8-2x^4-8\)

\(A=x^8-2x^4+4x^4-8\)

\(A=x^4\left(x^4-2\right)-4\left(x^4-2\right)\)

\(A=\left(x^4-4\right)\left(x^4-2\right)\)

\(a=\left(x^2-2\right)\left(x^2+2\right)\left(x^4-2\right)\)

26 tháng 7 2019

\(A=\left(x^4\right)^2-4x^4+2x^4-8\)

\(=x^4\left(x^4-4\right)+2\left(x^4-4\right)\)

\(=\left(x^4+2\right)\left(x^4-4\right)\)

\(=\left(x^4+2\right)\left(x^2+2\right)\left(x^2-2\right)\)

\(=\left(x^4+2\right)\left(x^2+2\right)\left(x-2\right)\left(x+2\right)\)

Bạn cũng có thể đặt \(t=x^4\)để bài toán dễ làm hơn

27 tháng 10 2018

a) \(x^4+4\)

\(=\left(x^2\right)^2+2\cdot x^2\cdot2+2^2-2\cdot x^2\cdot2\)

\(=\left(x^2+2\right)^2-\left(2x\right)^2\)

\(=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)

b) \(4x^8+1\)

\(=\left(2x^4\right)^2+2\cdot2x^4\cdot1+1^2-2\cdot2x^4\cdot1\)

\(=\left(2x^4+1\right)-\left(2x^2\right)^2\)

\(=\left(2x^4-2x^2+1\right)\left(2x^4+2x^2+1\right)\)

27 tháng 10 2018

a/ \(x^4+4=\left(x^2\right)^2+4x^2+4-4x^2=\left(x^2+2\right)^2-4x^2=\left(x^2-4x+2\right)\left(x^2+4x+2\right)\)

b/ \(4x^8+1=\left(2x^4\right)^2+1=\left(2x^4\right)^2+4x^4+1-4x^4=\left(2x^4+1\right)^2-4x^2=\left(2x^4-2x+1\right)\left(2x^4+2x+1\right)\)

\(x^8+x^4+1\)

\(=x^8+x^7+x^6-x^7-x^6-x^5+x^5+x^4+x^3-x^3-x^2-x+x^2+x+1\)

\(=\left(x^8+x^7+x^6\right)-\left(x^7+x^6+x^5\right)+\left(x^5+x^4+x^3\right)-\left(x^3+x^2+x\right)+\left(x^2+x+1\right)\)

\(=x^6\left(x^2+x+1\right)-x^5\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x\left(x^2+x+1\right)+\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x+1\right)\)

\(x^5-x^4-1\)

\(=x^5-x^4+x^3-x^3+x^2-x-x^2+x-1\)

\(=\left(x^5-x^4+x^3\right)-\left(x^3-x^2+x\right)-\left(x^2-x+1\right)\)

\(=x^3\left(x^2-x+1\right)-x\left(x^2-x+1\right)-\left(x^2-x+1\right)\)

\(=\left(x^2-x+1\right)\left(x^3-x-1\right)\)

25 tháng 10 2018

a) \(x^4+4\)

\(=\left(x^2\right)^2+2\cdot x^2\cdot2+2^2-2\cdot x^2\cdot2\)

\(=\left(x^2+2\right)^2-\left(2x\right)^2\)

\(=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)

b) \(4x^8+1\)

\(=\left(2x^4\right)^2+2\cdot2x^4\cdot1+1^2-2\cdot2x^4\cdot1\)

\(=\left(2x^4+1\right)^2-\left(2x^2\right)^2\)

\(=\left(2x^4-2x^2+1\right)\left(2x^4+2x^2+1\right)\)

25 tháng 10 2018

\(x^4+4\)

\(=\left(x^2\right)^2+2.x^2.2+2^2-2.x^2.2\)

\(=\left(x^2+2\right)^2-4x^2\)

\(=\left(x^2+2+2x\right)\left(x^2+2-2x\right)\)

23 tháng 6 2017

mk chỉ lm đc câu b thôi !

mk k viết đề đâu nha !:

=(x4-8x2+16)+(5x2-20x+20)+(3x2+12x+12)+15

=(x2-4)2+5(x-2)2+3(x-2)2+15

=[(x-2)2+3][(x-2)2+5]

=(x2-4x+7)(x2+4x+9)

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