Math Problem Solver

The sum of \(28 a b + 3 x\) and \(9 y z - 54 a\) is:

\[\begin{aligned}&=\left(28 a b + 3 x\right) + \left(9 y z - 54 a\right) \\\\ &= 28 a b - 54 a + 3 x + 9 y z \\\\ &= 28 a b - 54 a + 3 x + 9 y z \\\\\end{aligned}\]

The difference of \(28 a b + 3 x\) and \(9 y z - 54 a\) is:

\[\begin{aligned}&=\left(28 a b + 3 x\right) - \left(9 y z - 54 a\right) \\\\ &= 28 a b + 54 a + 3 x - 9 y z \\\\\end{aligned}\]

The product of \(28 a b + 3 x\) and \(9 y z - 54 a\) is:

\[\begin{aligned}&=\left(28 a b + 3 x\right) \cdot \left(9 y z - 54 a\right) \\\\ &= \left(- 54 a + 9 y z\right) \left(28 a b + 3 x\right) \\\\ &= - 1512 a^{2} b + 252 a b y z - 162 a x + 27 x y z \\\\\end{aligned}\]

The quotient of \(28 a b + 3 x\) and \(9 y z - 54 a\) is:

\[\begin{aligned}&= \frac{\left(28 a b + 3 x\right)}{\left(9 y z - 54 a\right)} \\\\ &= \frac{28 a b + 3 x}{- 54 a + 9 y z} \\\\ &= \frac{- 28 a b - 3 x}{9 \cdot \left(6 a - y z\right)} \\\\\end{aligned}\]