6a+7ab,2a+3b
MathBot Answer:
The sum of \(6 a + 7 a b\) and \(2 a + 3 b\) is:
\[\begin{aligned}&=\left(6 a + 7 a b\right) + \left(2 a + 3 b\right) \\\\ &= 7 a b + 8 a + 3 b \\\\\end{aligned}\]
The difference of \(6 a + 7 a b\) and \(2 a + 3 b\) is:
\[\begin{aligned}&=\left(6 a + 7 a b\right) - \left(2 a + 3 b\right) \\\\ &= 7 a b + 4 a - 3 b \\\\\end{aligned}\]
The product of \(6 a + 7 a b\) and \(2 a + 3 b\) is:
\[\begin{aligned}&=\left(6 a + 7 a b\right) \cdot \left(2 a + 3 b\right) \\\\ &= \left(2 a + 3 b\right) \left(7 a b + 6 a\right) \\\\ &= 14 a^{2} b + 12 a^{2} + 21 b^{2} a + 18 a b \\\\ &=a \left(14 a b + 12 a + 21 b^{2} + 18 b\right) \\\\\end{aligned}\]
The quotient of \(6 a + 7 a b\) and \(2 a + 3 b\) is:
\[\begin{aligned}&= \frac{\left(6 a + 7 a b\right)}{\left(2 a + 3 b\right)} \\\\ &= \frac{7 a b + 6 a}{2 a + 3 b} \\\\ &= \frac{a \left(7 b + 6\right)}{2 a + 3 b} \\\\\end{aligned}\]