Solve {l}{text{1.}5bx+5b}{text{3.}10xy+5xz}{text{5.}8a^{3}bc-12ab^3cd+4b^4c^2d^2}

$$\left. \begin{array} { l } { \text { 1. } 5 b x + 5 b } \\ { \text { 3. } 10 x y + 5 x z } \\ { \text { 5. } 8 a ^ { 3 } b c - 12 a b ^ { 3 } c d + 4 b ^ { 4 } c ^ { 2 } d ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$20bcx\left(x+1\right)\left(6y+z\right)\left(cd^{2}b^{3}-3adb^{2}+10a^{3}\right)$$

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.

$$20bcx\left(x+1\right)\left(6y+z\right)\left(cd^{2}b^{3}-3adb^{2}+10a^{3}\right)$$

Expand the expression.

$$120xyc^{2}d^{2}b^{4}-360acdxyb^{3}+1200bcxya^{3}+20xzc^{2}d^{2}b^{4}-60acdxzb^{3}+200bcxza^{3}+120yc^{2}d^{2}x^{2}b^{4}-360acdyx^{2}b^{3}+1200bcyx^{2}a^{3}+20zc^{2}d^{2}x^{2}b^{4}-60acdzx^{2}b^{3}+200bczx^{2}a^{3}$$

Evaluate

$$5b\left(x+1\right),\ 5x\left(6y+z\right),\ 4bc\left(cd^{2}b^{3}-3adb^{2}+10a^{3}\right)$$