Solve {l}{a+2a+9a}{m^{2}-2m^{2}-7m^{2}}{6x^{2}y^{2}-12x^{2}y^{2}+x^{2}y^{2}}{3a-2b-5b+9a}{a^2+b^2-2b^2-3a^2-a}

$$\left. \begin{array} { l } { a + 2 a + 9 a } \\ { m ^ { 2 } - 2 m ^ { 2 } - 7 m ^ { 2 } } \\ { 6 x ^ { 2 } y ^ { 2 } - 12 x ^ { 2 } y ^ { 2 } + x ^ { 2 } y ^ { 2 } } \\ { 3 a - 2 b - 5 b + 9 a } \\ { a ^ { 2 } + b ^ { 2 } - 2 b ^ { 2 } - 3 a ^ { 2 } - a } \end{array} \right.$$

Least Common Multiple

$$120a\left(7b-12a\right)\left(2a^{2}+b^{2}+a\right)\left(mxy\right)^{2}$$

Solution Steps

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

$$120a\left(7b-12a\right)m^{2}x^{2}y^{2}\left(2a^{2}+b^{2}+a\right)$$

Expand the expression.

$$840am^{2}x^{2}y^{2}b^{3}+1680bm^{2}x^{2}y^{2}a^{3}-1440a^{2}b^{2}m^{2}x^{2}y^{2}-2880m^{2}x^{2}y^{2}a^{4}+840ba^{2}m^{2}x^{2}y^{2}-1440m^{2}x^{2}y^{2}a^{3}$$

Evaluate

$$12a,\ -8m^{2},\ -5\left(xy\right)^{2},\ 12a-7b,\ -2a^{2}-b^{2}-a$$