Solve {l}{(-3xy+a)(3xy+a)}{(-1-2a^2b)(1-2a^2b)}

$$\left. \begin{array} { l } { ( - 3 x y + a ) ( 3 x y + a ) } \\ { ( - 1 - 2 a ^ { 2 } b ) ( 1 - 2 a ^ { 2 } b ) } \end{array} \right.$$

Least Common Multiple

$$-\left(9\left(xy\right)^{2}-a^{2}\right)\left(4\left(ba^{2}\right)^{2}-1\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$-9x^{2}y^{2}+a^{2}=\left(-3xy-a\right)\left(3xy-a\right) -1+4a^{4}b^{2}=\left(2ba^{2}-1\right)\left(2ba^{2}+1\right)$$

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

$$\left(3xy-a\right)\left(3xy+a\right)\left(-2ba^{2}-1\right)\left(2ba^{2}-1\right)$$

Expand the expression.

$$-36b^{2}x^{2}y^{2}a^{4}+9x^{2}y^{2}+4b^{2}a^{6}-a^{2}$$

Evaluate

$$a^{2}-9\left(xy\right)^{2},\ 4b^{2}a^{4}-1$$