Solve {l}{(3p+2q)^2-3p(p+4q)}{Aquad6p^2+4q^2}

$$\left. \begin{array} { l } { ( 3 p + 2 q ) ^ { 2 } - 3 p ( p + 4 q ) } \\ { A \quad 6 p ^ { 2 } + 4 q ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$2\left(3p^{2}+2q^{2}\right)\left(A_{6}p^{2}+4q^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$6p^{2}+4q^{2}=2\left(3p^{2}+2q^{2}\right)$$

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

$$2\left(3p^{2}+2q^{2}\right)\left(A_{6}p^{2}+4q^{2}\right)$$

Expand the expression.

$$6A_{6}p^{4}+4A_{6}p^{2}q^{2}+24p^{2}q^{2}+16q^{4}$$

Evaluate

$$6p^{2}+4q^{2},\ A_{6}p^{2}+4q^{2}$$