Solve {l}{x^{3}divx}{84a^{2}b^5div12a^2b^2}{-40x-30by-10}{10a^3+12abtext{by}2a}

$$\left. \begin{array} { l } { x ^ { 3 } \div x } \\ { 84 a ^ { 2 } b ^ { 5 } \div 12 a ^ { 2 } b ^ { 2 } } \\ { - 40 x - 30 b y - 10 } \\ { 10 a ^ { 3 } + 12 a b \text { by } 2 a } \end{array} \right.$$

Least Common Multiple

$$70x^{2}\left(4x+3by+1\right)\left(12yb^{2}+5a\right)a^{4}b^{7}$$

Solution Steps

Factor the expressions that are not already factored.

$$-40x-30by-10=10\left(-4x-3by-1\right) 10a^{3}+24a^{2}yb^{2}=2a^{2}\left(12yb^{2}+5a\right)$$

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

$$70x^{2}\left(4x+3by+1\right)\left(12yb^{2}+5a\right)a^{4}b^{7}$$

Expand the expression.

$$1400x^{3}a^{5}b^{7}+2520x^{2}y^{2}a^{4}b^{10}+350x^{2}a^{5}b^{7}+3360yx^{3}a^{4}b^{9}+840yx^{2}a^{4}b^{9}+1050yx^{2}a^{5}b^{8}$$

Evaluate

$$x^{2},\ 7a^{4}b^{7},\ -40x-30by-10,\ 24y\left(ab\right)^{2}+10a^{3}$$