Solve {l}{25x^2-10x}{+1-9y^2}{6y^2-z^2}

$$\left. \begin{array} { l } { 25 x ^ { 2 } - 10 x } \\ { + 1 - 9 y ^ { 2 } } \\ { 6 y ^ { 2 } - z ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$5x\left(5x-2\right)\left(9y^{2}-1\right)\left(z^{2}-6y^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$1-9y^{2}=\left(-3y-1\right)\left(3y-1\right)$$

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

$$5x\left(3y-1\right)\left(5x-2\right)\left(3y+1\right)\left(z^{2}-6y^{2}\right)$$

Expand the expression.

$$-1350x^{2}y^{4}+225x^{2}y^{2}z^{2}+150x^{2}y^{2}-25x^{2}z^{2}+540xy^{4}-90xy^{2}z^{2}-60xy^{2}+10xz^{2}$$

Evaluate

$$5x\left(5x-2\right),\ 1-9y^{2},\ 6y^{2}-z^{2}$$