Giải câu 1 trang 19 toán VNEN 8 tập 1.
a) 5x - 15y = 5(x - 3y);
b) $\frac{3}{5}$x$^{2}$ + 5x$^{4}$ - x$^{2}$y = x$^{2}$($\frac{3}{5}$ + 5x$^{2}$ - y);
c) 14x$^{2}$y$^{2}$ - 21xy$^{2}$ + 28x$^{2}$y = 7xy(2xy - 3y + 4x);
d) $\frac{2}{7}$x(3y - 1) - $\frac{2}{7}$y(3y - 1) = $\frac{2}{7}$(3y - 1)(x - y);
e) x$^{3}$ - 3x$^{2}$ + 3x - 1 = x$^{3}$ - 3.x$^{2}$.1 + 3.x.1$^{2}$ - 1 = (x - 1)$^{3}$;
f) (x + y)$^{2}$ - 4x$^{2}$ = (x + y)$^{2}$ - (2x)$^{2}$ = (x + y - 2x)(x + y + 2x) = (-x + y)(3x + y);
g) 27x$^{3}$ + $\frac{1}{8}$ = (3x)$^{3}$ + ($\frac{1}{2}$)$^{3}$ = (3x + $\frac{1}{2}$)(9x$^{2}$ - $\frac{3}{2}$x + $\frac{1}{4}$);
h) ( x + y)$^{3}$ - (x - y)$^{3}$ = [(x + y) - (x - y)][(x + y)$^{2}$ + (x + y)(x - y) + (x - y)$^{2}$]
= 2y(x$^{2}$ + 2xy + y$^{2}$ + x$^{2}$ - y$^{2}$ + x$^{2}$ - 2xy + y$^{2}$) = 2y(3x$^{2}$ + y$^{2}$).