a: \(A=x\sqrt{x}-y\sqrt{y}+x\sqrt{y}-y\sqrt{x}\)

\(=\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)+\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)\)

\(=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)^2\)

b: \(B=5x^2-7x\sqrt{y}+2y\)

\(=5x^2-5x\sqrt{y}-2x\sqrt{y}+2y\)

\(=5x\left(x-\sqrt{y}\right)-2\sqrt{y}\left(x-\sqrt{y}\right)\)

\(=\left(x-\sqrt{y}\right)\left(5x-2\sqrt{y}\right)\)

\(-2x^4-7x^3-x^2+7x+3\)

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

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

\(=-\left(x+1\right)\left[2x^2\left(x-1\right)+7x\left(x-1\right)+3\left(x-1\right)\right]\)

\(=-\left(x+1\right)\left(x-1\right)\left(2x^2+7x+3\right)\)

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

=> x (x³ + 5x² - 7x - 41)

      \(x^4+6x^3+7x^2-6x+1\)

\(=x^4+6x^3+9x^2-2x^2-6x+1\)

\(=\left(x^2\right)^2+2.x^2.3x+\left(3x\right)^2-2\left(x^2+3x\right)+1\)

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

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

Chúc bạn học tốt.

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

\(=x^4+6x^3+9x^2-2x^2-6x+1\)

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

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

https://olm.vn/hoi-dap/tim-kiem?q=Cho+%CE%94ABC+vu%C3%B4ng+t%E1%BA%A1i+A+c%C3%B3+AB+%3E+AC,+M+l%C3%A0+%C4%91i%E1%BB%83m+tu%E1%BB%B3+%C3%BD+tr%C3%AAn+BC.+Qua+M+k%E1%BA%BB+Mx+vu%C3%B4ng+g%C3%B3c+v%E1%BB%9Bi+BC+v%C3%A0+c%E1%BA%AFt+AB+t%E1%BA%A1i+I+c%E1%BA%AFt+CA+t%E1%BA%A1i+D.a.+Ch%E1%BB%A9ng+minh+%CE%94ABC+%C4%91%E1%BB%93ng+d%E1%BA%A1ng+v%E1%BB%9Bi+%CE%94MDCb.+Ch%E1%BB%A9ng+minh:+BI.BA+=+BM.BCc.+Cho+g%C3%B3c+ACB+=+60o+v%C3%A0+S%CE%94CDB+=+60+cm2.+T%C3%ADnh+S%CE%94CMAGi%C3%BAp+m%C3%ACnh+c%C3%A2u+c+v%E1%BB%9Bi&id=573451

x^4+6x^3+7x^2–6x+1

=x^4+(6x^3–2x^2)+(9x^2–6x+1)

= x^4+2x^2(3x–1)+(3x–1)^2

=(x^2+3x–1)^2

Ta có `:`

`x^3 - 7x-6`

`= x^3 - 9x + 2x - 6`

`= x( x^2 - 9 ) + 2( x-3 )`

`= x( x-3 )( x + 3 ) + 2( x-3 )`

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

`= ( x^2 + 3x + 2 )( x-3 )`

`= ( x^2 + 2x + x + 2 )( x-3 )`

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

`= ( x+1)(x+2)(x-3)`  

hãy giúp mình đi ạ `bb!` 

TƯƠNG TỰ CÁC BÀI TRONG NÂNG CAO PHÁT TRIỂN 8

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

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

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

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

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

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

= x⁴ - x³ + x² - 5x³ + 5x² - 5x + x² - x +1  = x² ( x² - x +1 ) - 5x ( x² - x +1 ) + x² - x +1 = ( x² - x +1 ) ( x² - 5x + 1 )

mk ko biết