x² - axy - bxy + aby² 

= ( x² - axy) - ( bxy - aby²)

= x( x-ay) - by( x - ay)

= ( x-ay)( x - by)

Bạn chuyển tất cả hạng tử từ vế phải sang vế trái ta được

\(^{x^2+5\text{x}^3+x^2y=5\text{x}^3+x^2y}\)

\(x^2+5\text{x}^3+x^2y-5\text{x}^3-x^2y=0\)

Rút gọn ta được

\(x^2=0\)

\(=>x=0\)

tick cho mình nha

\(\left(x-5\right)\left(x-1\right)\left(x+3\right)\left(x+7\right)+60\)

\(=\left(x^2+2x-35\right)\left(x^2+2x-3\right)+60\)

\(=\left(x^2+2x\right)^2-38\left(x^2+2x\right)+105+60\)

\(=\left(x^2+2x\right)^2-3\left(x^2+2x\right)-35\left(x^2+2x\right)+165\)

\(=\left(x^2+2x-3\right)\left(x^2+2x-35\right)\)

\(=\left(x+3\right)\left(x-1\right)\left(x+7\right)\left(x-5\right)\)

7x-7y+ax-ay=(7x-7y)+(ax-ay)=7(x-y)+a(x-y)=(x-y)(7+a)

7x-7y+ax-ay

=(7x-7y)+(ax-ay)

=7(x-y)+a(x-y)

=(x-y)(7+a)

Ta có : x⁸ + x + 1 

= x⁸ + x⁷ - x⁷ - x⁶ + x⁶ + x⁵ - x⁵ - x⁴ + x⁴ + x³ - x³ - x² + x² - x - 1 + x + 1 + x + 1

=  (x⁸ + x⁷) - (x⁷ + x⁶) + (x⁶ + x⁵) - (x⁵ + x⁴) + (x⁴ + x³) - (x³ + x²) + (x² + x) + (x + 1)

= x⁷(x + 1) - x⁶(x + 1) + x⁵(x + 1) - x⁴(x + 1) + x³(x + 1) - x²(x + 1) + x(x + 1) + (x + 1)

= (x + 1)(x⁷ - x⁶ + x⁵ - x⁴ + x³ - x² + x + 1)

(mk ko chắc lắm)

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

x⁴ - x³ - x + 1

= (x⁴ - x³) - (x - 1)

= x³(x - 1) - (x - 1)

= (x³ - 1)(x - 1)