bn chép lại đề nha

\(=x^4-x+1997\left(x^2+x+1\right)\)

\(=x\left(x-1\right)\left(x^2+x+1\right)+1997\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+1997\right)\)

xong nha. chúc bn hc tốt

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

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

Ta có : \(x^4-5x^2+4\)

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

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

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

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

Ta có: \(x^4-5x^2+4\)

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

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

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

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

${}^{}-2{}^{}+2x-1$

$={}^{}-{}^{}-{}^{}+{}^{}-{}^{}+x+x-1$

$={}^{}\left(x-1\right)-{}^{}\left(x-1\right)-x\left(x-1\right)+\left(x-1\right)$

$=\left(x-1\right)\left({}^{}-{}^{}-x+1\right)$
$=\left(x-1\right)[$

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

\(x^4+2x^3+2x^2+2x+1\)

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

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

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

\(=\left(x+1\right)^2\cdot\left(x^2+1\right)\)

= (x⁴ + x³ + x²) + (1997x² + 1997x + 1997) - (x³ + x² + x)

= x²(x² + x + 1) + 1997(x² + x + 1) - x(x² + x + 1)

= (x² + x + 1)(x² - x + 1997)

a) x⁴ + 1997x² + 1996x +1997

= x⁴ + 1997x² + 1997x - x +1997

=(x⁴-x) + (1997x² +1997x+1997)

=x(x³-1) + 1997(x²+x+1)

=x(x-1)(x²+x+1) + 1997(x²+x+1)

=(x²+x+1)(x²-x) + 1997(x²+x+1)

=(x²+x+1)(x²-x+1997)

b) x² -x -2001.2002

=x² - x -2002² +2002

=(x²-2002²)-(x-2002)

=(x-2002)(x+2002) - (x-2002)

=(x-2002)(x+2002+1)

=(x-2002)(x+2003)

c)x⁸ + 98x⁴ +1

= (x⁸+2x⁴+1) + 96x⁴

= (x⁴+1)² + 96x⁴

=[(x⁴+1)² + 2.(x⁴+1).8 + 64x⁴ ]+[32x⁴ - 16x²(x⁴+1)]

=(x⁴+1+8x²)-16x²(-2x²+x⁴+1)

=(x⁴+8x²+1)²- 16x²(x²-1)²

=(x⁴ + 8x² +1)²- [4x(x²-1)]²

=(x⁴+8x²+1)² - (4x³-4x)²

=(x⁴-4x³+8x²+4x+1)(x⁴+4x³+8x²-4x+1)

mn giúp mình vs mik đang cần gấp

Bạn tự làm cho trung thực đừng dựa vào người khác

Nếu ai thấy những gì mình nói là đúng thì nhớ k nha

Thanks

vương tuấn khải ko biết thì hỏi thôi bn ko giúp thì thôi lại còn bình luận này nọ

\(a^2-4b^2\)

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

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

a) \(a^2-4b^2\)

= \(\left(a-4b\right).\left(a+4b\right)\)

= \(a^2\)