Solve {l}{16a^3+54b^3}{x^2+8x+16-3xy-12y}

$$\left. \begin{array} { l } { 16 a ^ { 3 } + 54 b ^ { 3 } } \\ { x ^ { 2 } + 8 x + 16 - 3 x y - 12 y } \end{array} \right.$$

Least Common Multiple

$$-2\left(x+4\right)\left(x-3y+4\right)\left(8a^{3}+27b^{3}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$16a^{3}+54b^{3}=2\left(2a+3b\right)\left(4a^{2}-6ab+9b^{2}\right) 16+8x-12y+x^{2}-3xy=\left(x+4\right)\left(x-3y+4\right)$$

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

$$-2\left(x+4\right)\left(x-3y+4\right)\left(2a+3b\right)\left(9b^{2}+4a^{2}-6ab\right)$$

Expand the expression.

$$-54x^{2}b^{3}-16x^{2}a^{3}+48xya^{3}+162xyb^{3}-432xb^{3}-128xa^{3}+192ya^{3}+648yb^{3}-864b^{3}-256a^{3}$$

Evaluate

$$2\left(8a^{3}+27b^{3}\right),\ \left(x+4\right)\left(x-3y+4\right)$$