\(f\left(x\right)=x^7-90x^6+90x^5-90x^4+...+90x+1928\)\(\Rightarrow f\left(89\right)=x^7-\left(x+1\right)x^6+\left(x+1\right)x^5\)\(-\left(x+1\right)x^4+...+\left(x+1\right)x+1928\)

\(\Rightarrow f\left(89\right)=x^7-x^7-x^6+x^6+x^5-x^5\)\(-x^4+...+\)\(x^2+x+1928\)\(=89+1928=2017\)

2017

\(90x-6750=75x-x^2\)
\(\Leftrightarrow180x-6750=75x-x^2\)
\(\Leftrightarrow x^2+105x-6750=0\)
\(\Leftrightarrow x^2-45x+150x-6750=0\)
\(\Leftrightarrow\left(x-45\right)\left(x+150\right)=0 \)
\(\Leftrightarrow\left[{}\begin{matrix}x-45=0\\x+150=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=45\\x=-150\end{matrix}\right.\)
Vậy x=45 hoặc x=-150

a, \(\left(x+2\right)^3-x\left(x^2+6x-3\right)=0\Leftrightarrow x^3+4x^2+4x+2x^2+8x+8-x^3-6x^2+3x=0\)

\(\Leftrightarrow15x+8=0\Leftrightarrow x=-\frac{8}{15}\)

b, \(\left(x+4\right)^3-x\left(x+6\right)^2=7\Leftrightarrow12x+64=0\Leftrightarrow x=-\frac{19}{4}\)làm tắt:P 

Tự làm nốt nhé 

dễ vãi lol ra bn ngu vãi đái

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

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

b, \(x^6+y^6=\left(x^2\right)^3+\left(y^2\right)^3=\left(x^2+y^2\right)\left(x^4-x^2y^2+y^4\right)\)

c, \(x^{16}-1=\left(x^2\right)^8-1=\left[\left(x^2\right)^4\right]^2-1=\left(x^8-1\right)\left(x^8+1\right)\)

Phân tích à :)

a) ( x - y + 4 )² - ( 2x + 3y - 1 )²

= [ ( x - y + 4 ) - ( 2x + 3y - 1 ) ][ ( x - y + 4 ) + ( 2x + 3y - 1 ) ]

= ( x - y + 4 - 2x - 3y + 1 )( x - y + 4 + 2x + 3y - 1 )

= ( -x - 4y + 5 )( 3x + 2y + 3 )

b) x⁶ + y⁶ = ( x² )³ + ( y² )³ = ( x² + y² )( x⁴ - x²y² + y⁴ )

c) x¹⁶ - 1 = ( x⁸ )² - 1² = ( x⁸ - 1 )( x⁸ + 1 )

= ( x⁴ - 1 )( x⁴ + 1 )( x⁸ + 1 )

= ( x² - 1 )( x² + 1 )( x⁴ + 1 )( x⁸ + 1 )

= ( x - 1 )( x + 1 )( x² + 1 )( x⁴ + 1 )( x⁸ + 1 )

d) x³⁶ - 64 = ( x¹⁸ )² - 8²

= ( x¹⁸ - 8 )( x¹⁸ + 8 )

= ( x⁶ - 2 )( x¹² + 2x + 4 )( x⁶ + 2 )( x¹² - 2x + 4 )

e) 9x² + 90x + 225 - ( x - 7 )²

= ( 3x + 15 )² - ( x - 7 )²

= ( 3x + 15 - x + 7 )( 3x + 15 + x - 7 )

= ( 2x + 22 )( 2x - 8 )

= 2( x + 11 ).2( x - 4 )

= 4( x + 11 )( x - 4 )

f) 49( y - 4 )² - 9y² - 36y - 36

= 7²( y - 4 )² - ( 9y² + 36y + 36 )

= ( 7y - 28 )² - ( 3y + 6 )² 

= ( 7y - 28 - 3y - 6 )( 7y - 28 + 3y + 6 )

= ( 4y - 34 )( 10y - 22 )

= 2( 2y - 17 ).2( 5y - 11 )

= 4( 2y - 17 )( 5y - 11 )

giúp mifnnh với ạ !!

CHữ số hay tích

dễ cậu kêu ai trả lời được cho 2 k

a) =( x²+y²-5)²-[2(xy-2)]²

⁼( x²+y²-5)²- (2xy-4)²

=(x²+y²-5+2xy-4)(x²+y²-5-2xy+4)

=[(x+y)²-9][(x-y)²-1]

phân tích tiếp HĐT 2 ở 2 thừa số

\(=\left(3x+15\right)^2-\left(x-7\right)^2=\left(4x+8\right)\left(2x+22\right)=8\left(x+2\right)\left(x+11\right)\)

(x-7)^2 = x^2-14x+49 

<=> 9x^2+90x+225 -x^2+14x-49 
= 8x^2+104x+176 
= 8(x^2+13+22) 
<=> 8(x+2)(x+11)

9x²+90x+225-(x-7)²

=(3x+15)²-(x-7)²

=(3x+15-x+7)(3x+15+x-7)

=(2x+22)(4x+8)

=2 (x+11)4 (x+2)

=8 (x+11)(x+2)

\(=x^4-9x^3+9x^3-81x^2-9x^2+81x+10x-90\)

\(=\left(x-9\right)\left(x^3+9x^2-9x+10\right)\)

\(=\left(x-9\right)\left(x^3+10x^2-x^2-10x+x+10\right)\)

\(=\left(x-9\right)\left(x+10\right)\left(x^2-x+1\right)\)