x*3 + 2x*2 - 4x - 8, 2x*3 + 7x*2 + 4x - 4
MathBot Answer:
The sum of \(x \cdot 3 + 2 x \cdot 2 - 4 x - 8\) and \(2 x \cdot 3 + 7 x \cdot 2 + 4 x - 4\) is:
\[\begin{aligned}&=\left(x \cdot 3 + 2 x \cdot 2 - 4 x - 8\right) + \left(2 x \cdot 3 + 7 x \cdot 2 + 4 x - 4\right) \\\\ &= \left(-1\right) 4 x + 4 x + 3 x 3 + 9 x 2 - 12 \\\\ &= 27 x - 12 \\\\\end{aligned}\]
The difference of \(x \cdot 3 + 2 x \cdot 2 - 4 x - 8\) and \(2 x \cdot 3 + 7 x \cdot 2 + 4 x - 4\) is:
\[\begin{aligned}&=\left(x \cdot 3 + 2 x \cdot 2 - 4 x - 8\right) - \left(2 x \cdot 3 + 7 x \cdot 2 + 4 x - 4\right) \\\\ &= \left(-5\right) x 2 - 4 x - 4 x - x 3 - 4 \\\\ &= - 21 x - 4 \\\\\end{aligned}\]
The product of \(x \cdot 3 + 2 x \cdot 2 - 4 x - 8\) and \(2 x \cdot 3 + 7 x \cdot 2 + 4 x - 4\) is:
\[\begin{aligned}&=\left(x \cdot 3 + 2 x \cdot 2 - 4 x - 8\right) \cdot \left(2 x \cdot 3 + 7 x \cdot 2 + 4 x - 4\right) \\\\ &= \left(4 x + 2 x 3 + 7 x 2 - 4\right) \left(- 4 x + x 3 + 2 x 2 - 8\right) \\\\ &= 72 x^{2} - 204 x + 32 \\\\\end{aligned}\]
The quotient of \(x \cdot 3 + 2 x \cdot 2 - 4 x - 8\) and \(2 x \cdot 3 + 7 x \cdot 2 + 4 x - 4\) is:
\[\begin{aligned}&= \frac{\left(x \cdot 3 + 2 x \cdot 2 - 4 x - 8\right)}{\left(2 x \cdot 3 + 7 x \cdot 2 + 4 x - 4\right)} \\\\ &= \frac{- 4 x + x 3 + 2 x 2 - 8}{4 x + 2 x 3 + 7 x 2 - 4} \\\\ &= \frac{3 x - 8}{4 \cdot \left(6 x - 1\right)} \\\\\end{aligned}\]