Solve {l}{5(2x+1)(3x+5)div(2x+1)}{26xy(x+5)(y-4)div13x(y-4)}

$$\left. \begin{array} { l } { 5 ( 2 x + 1 ) ( 3 x + 5 ) \div ( 2 x + 1 ) } \\ { 26 x y ( x + 5 ) ( y - 4 ) \div 13 x ( y - 4 ) } \end{array} \right.$$

Least Common Multiple

$$10y\left(x+5\right)\left(3x+5\right)\left(x\left(y-4\right)\right)^{2}$$

Solution Steps

Factor the expressions that are not already factored.

$$15x+25=5\left(3x+5\right)$$

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$10y\left(x+5\right)\left(3x+5\right)x^{2}\left(y-4\right)^{2}$$

Expand the expression.

$$200x^{3}y^{3}+250x^{2}y^{3}-2000x^{2}y^{2}+30y^{3}x^{4}-240y^{2}x^{4}-1600y^{2}x^{3}+480yx^{4}+3200yx^{3}+4000yx^{2}$$

Evaluate

$$5\left(3x+5\right),\ 2y\left(x+5\right)\left(x\left(y-4\right)\right)^{2}$$