Solve {l}{25-15b+9b^{2}}{(m^{2}+2)^2-12(m^2+2)+36}{x^2+6ax+9a^2}

$$\left. \begin{array} { l } { 25 - 15 b + 9 b ^ { 2 } } \\ { ( m ^ { 2 } + 2 ) ^ { 2 } - 12 ( m ^ { 2 } + 2 ) + 36 } \\ { x ^ { 2 } + 6 a x + 9 a ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$\left(9b^{2}-15b+25\right)\left(\left(x+3a\right)\left(m^{2}-4\right)\right)^{2}$$

Solution Steps

Factor the expressions that are not already factored.

$$\left(m^{2}-4\right)^{2}=\left(m-2\right)^{2}\left(m+2\right)^{2}$$

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

$$\left(x+3a\right)^{2}\left(9b^{2}-15b+25\right)\left(m^{2}-4\right)^{2}$$

Expand the expression.

$$9b^{2}x^{2}m^{4}-15bx^{2}m^{4}-72b^{2}m^{2}x^{2}+25x^{2}m^{4}+120bm^{2}x^{2}+144b^{2}x^{2}-200m^{2}x^{2}-240bx^{2}+400x^{2}+54axb^{2}m^{4}-90abxm^{4}-432axb^{2}m^{2}+150axm^{4}+720abxm^{2}+864axb^{2}-1200axm^{2}-1440abx+2400ax+81a^{2}b^{2}m^{4}-135ba^{2}m^{4}-648a^{2}b^{2}m^{2}+225a^{2}m^{4}+1080ba^{2}m^{2}+1296a^{2}b^{2}-1800a^{2}m^{2}-2160ba^{2}+3600a^{2}$$

Evaluate

$$9b^{2}-15b+25,\ \left(m^{2}-4\right)^{2},\ \left(x+3a\right)^{2}$$