Solve {l}{a^2(4a-3)^2-a(4a-3)^3}{10px-15py+6xy-9y^2}

$$\left. \begin{array} { l } { a ^ { 2 } ( 4 a - 3 ) ^ { 2 } - a ( 4 a - 3 ) ^ { 3 } } \\ { 10 p x - 15 p y + 6 x y - 9 y ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$3a\left(1-a\right)\left(2x-3y\right)\left(3y+5p\right)\left(4a-3\right)^{2}$$

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.

$$3a\left(1-a\right)\left(2x-3y\right)\left(3y+5p\right)\left(4a-3\right)^{2}$$

Expand the expression.

$$-288xya^{4}+720xya^{3}-594xya^{2}+162axy-480pxa^{4}+1200pxa^{3}-990pxa^{2}+270apx+432y^{2}a^{4}-1080y^{2}a^{3}+891a^{2}y^{2}-243ay^{2}+720pya^{4}-1800pya^{3}+1485pya^{2}-405apy$$

Evaluate

$$3a\left(1-a\right)\left(4a-3\right)^{2},\ \left(2x-3y\right)\left(3y+5p\right)$$