\(P=x^2\left(b-c\right)+b^2\left(c-x\right)+c^2\left(x-b\right)\) thành nhân tử...">
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2 tháng 7 2019

P=x^2(b-c)+b^2(c-x)+c^2(x-b)
P=X^2(b-c)+b^2[-(b-c)-(x-b)]+c^2(x-b)
P=x^2(b-c)-b^2(b-c)-b^2(x-b)+c^2(x-b)
P=(x^2-b^2)(b-c)- (b^2-c^2)(x-b)
P=(x+b)(x-b)(b-c)-(b+c)(b-c)(x-b)
P=(x-b)(b-c)(x+b-b-c)
P=(x-b)(b-c)(x-c)

28 tháng 9 2017

bạn viết so mu nhu the nao day ?

28 tháng 9 2017

a)x2-2xy+y2+3x-3y-10

=(x2-2xy+y2)+(3x-3y)-10

=(x-y)2+3(x-y)-10

=(x-y).(x-y+3)-10

b mk thấy nó sai đề sao ý 

c) \(C=\left(x^2+x+4\right)^2+8x\left(x^2+x+4\right)+15x^2\)

\(=\left(x^2+x+4\right)^2+2.4x.\left(x^2+x+4\right)+16x^2-x^2\)

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

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

\(=\left(x^2+5x+4-x\right)\left(x^2+5x+4+x\right)=\left(x^2+4x+4\right)\left(x^2+6x+4\right)\)

1 tháng 10 2017

a)\(a\left(b^3-c^3\right)+b\left(c^3-a^3\right)+c\left(a^3-b^3\right)\)

\(=a\left(b^3-c^3\right)-b\text{[}\left(b^3-c^3\right)+\left(a^3-b^3\right)\text{]}+c\left(a^3-b^3\right)\)

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

\(=\left(a-b\right)\left(b^3-c^3\right)-\left(b-c\right)\left(a^3-b^3\right)\)

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

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

\(=\left(a-b\right)\left(b-c\right)\left(c-a\right)\left(a+b+c\right)\)

1 tháng 1 2022

a) \(x^7+x^5+1\)

\(=x^7-x+x^5-x^2+x^2+x+1\)

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

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

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

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

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

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

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

b) \(x^5-x^4-1\)

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

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

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

22 tháng 5 2018

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

b)\(\left(1-2a+a^2\right)-\left(b^2-2bc+c^2\right)=\left(1-a\right)^2-\left(b-c\right)^2=\)\(\left(1-a+b-c\right)\left(1-a-b+c\right)\)

22 tháng 5 2018

lm tiếp câu c

c)  \(C=\left(x-7\right)\left(x-5\right)\left(x-4\right)\left(x-2\right)-72\)

\(=\left[\left(x-7\right)\left(x-2\right)\right]\left[\left(x-5\right)\left(x-4\right)\right]-72\)

\(=\left(x^2-9x+14\right)\left(x^2-9x+20\right)-72\)

Đặt   \(x^2-9x+17=a\) ta có:

        \(C=\left(a-3\right)\left(a+3\right)-72\)

            \(=a^2-9-72\)

           \(=a^2-81=\left(a-9\right)\left(a+9\right)\)
Thay trở lại ta được:  \(C=\left(x^2-9x++8\right)\left(x^2-9x+26\right)\)