Question

Divide as directed.

(i)$5(2x+1)(3x+5)÷(2x+1)$

(ii)$26xy(x+5)(y-4)÷13x(y-4)$

(iii)$52pqr(p+q)(q+r)(r+p)÷104pq(q+r)(r+p)$

(iv)$20(y+4)(y^2+5y+3)÷5(y+4)$

(v)$x(x+1)(x+2)(x+3)÷x(x+1)$

Answer 1

(i)$5(2x+1)(3x+5)÷(2x+1)$

$=\frac{5(2x+1)(3x+5)}{(2x+1)}$

$=\frac{5(3x+5)}{1}$

$\therefore 5(2x+1)(3x+5)÷(2x+1)=5(3x+5)$

(ii)$26xy(x+5)(y-4)÷13x(y-4)$

$=\frac{26xy(x+5)(y-4)}{13x(y-4)}$

$=\frac{2y(x+5)(y-4)}{(y-4)}$

$=\frac{2y(x+5)}{1}$

$\therefore (x+5)(y-4)÷13x(y-4)=2y(x+5)$

(iii)$52pqr(p+q)(q+r)(r+p)÷104pq(q+r)(r+p)$

$=\frac{52pqr(p+q)(q+r)(r+p)}{104pq(q+r)(r+p)}$

$=\frac{pqr(p+q)(q+r)(r+p)}{pq(q+r)(r+p)}$

$=\frac{r(p+q)(q+r)(r+p)}{(q+r)(r+p)}$

$=\frac{r(p+q)(r+p)}{(r+p)}$

$=\frac{r(p+q)}{1}$

$\therefore 52pqr(p+q)(q+r)(r+p)÷104pq(q+r)(r+p)=r(p+q)$

(iv)$20(y+4)(y^2+5y+3)÷5(y+4)$

$=\frac{20(y+4)(y^2+5y+3)}{5(y+4)}$

$=\frac{4(y+4)(y^2+5y+3)}{(y+4)}$

$=\frac{4(y^2+5y+3)}{1}$

$\therefore 20(y+4)(y^2+5y+3)÷5(y+4)=4(y^2+5y+3)$

(v)$x(x+1)(x+2)(x+3)÷x(x+1)$

$=\frac{x(x+1)(x+2)(x+3)}{x(x+1)}$

$=\frac{(x+1)(x+2)(x+3)}{(x+1)}$

$=\frac{(x+2)(x+3)}{1}$

$\therefore x(x+1)(x+2)(x+3)÷x(x+1)=(x+2)(x+3)$