Solve {l}{49-a^{2}+8ab-16b^2}{9b^2-16c^2-12ab+4a^2}

$$\left. \begin{array} { l } { 49 - a ^ { 2 } + 8 a b - 16 b ^ { 2 } } \\ { 9 b ^ { 2 } - 16 c ^ { 2 } - 12 a b + 4 a ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$\left(-\left(4b-a\right)^{2}+49\right)\left(\left(2a-3b\right)^{2}-16c^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$-a^{2}-16b^{2}+8ab+49=\left(a-4b-7\right)\left(-a+4b-7\right) -16c^{2}+\left(3b-2a\right)^{2}=\left(2a-3b-4c\right)\left(2a-3b+4c\right)$$

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

$$\left(a-4b-7\right)\left(-a+4b-7\right)\left(2a-3b-4c\right)\left(2a-3b+4c\right)$$

Expand the expression.

$$-4a^{4}-169a^{2}b^{2}+16a^{2}c^{2}+196a^{2}+264ab^{3}-128abc^{2}-588ab-144b^{4}+256b^{2}c^{2}+441b^{2}+44ba^{3}-784c^{2}$$

Evaluate

$$-\left(a-4b\right)^{2}+49,\ \left(3b-2a\right)^{2}-16c^{2}$$