Solve {l}{12x+(5-3x)}{(15x+6y)+(8x-17y)}{(12a-14)-26a}{(10p-5q)-(16q+4p)-5p}{12a-(-3b-15a)}

$$\left. \begin{array} { l } { 12 x + ( 5 - 3 x ) } \\ { ( 15 x + 6 y ) + ( 8 x - 17 y ) } \\ { ( 12 a - 14 ) - 26 a } \\ { ( 10 p - 5 q ) - ( 16 q + 4 p ) - 5 p } \\ { 12 a - ( - 3 b - 15 a ) } \end{array} \right.$$

Least Common Multiple

$$42\left(a+1\right)\left(p-21q\right)\left(9x+5\right)\left(23x-11y\right)\left(b+9a\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$-14-14a=14\left(-a-1\right) 27a+3b=3\left(9a+b\right)$$

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

$$42\left(a+1\right)\left(p-21q\right)\left(9x+5\right)\left(23x-11y\right)\left(b+9a\right)$$

Expand the expression.

$$8694abpx^{2}+78246pa^{2}x^{2}-182574abqx^{2}-1643166qa^{2}x^{2}+8694bpx^{2}+78246apx^{2}-1643166aqx^{2}-182574bqx^{2}+87318abqxy+785862qxya^{2}-4158abpxy-37422pxya^{2}+4830abpx+87318bqxy+785862aqxy-101430abqx-37422apxy-4158bpxy+43470pxa^{2}-912870qxa^{2}+4830bpx+43470apx-912870aqx-101430bqx+48510abqy+436590qya^{2}-2310abpy-20790pya^{2}+48510bqy+436590aqy-20790apy-2310bpy$$

Evaluate

$$9x+5,\ 23x-11y,\ -14a-14,\ p-21q,\ 3b+27a$$