Hcf of a(a+b) a^2(a^2-b^2)a(a-b)
You asked:
Find the polynomial greatest common divisor of the following expressions: \(a \left(a + b\right)\), \(a^{2} a \left(a^{2} - b^{2}\right) \left(a - b\right)\)
MathBot Answer:
The greatest common divisor is \(a^{2} + a b\).
Begin by factoring all expressions completely. $$\begin{aligned}a \left(a + b\right) &= a \cdot \left(a + b\right)\\a^{2} a \left(a^{2} - b^{2}\right) \left(a - b\right) &= a^{3} \left(a - b\right)^{2} \left(a + b\right)\\\end{aligned}$$
Find the greatest common divisor by multiplying common factors together, including only the lowest power of those factors which are common to all expressions. \[\operatorname{gcd}(a \left(a + b\right), a^{2} a \left(a^{2} - b^{2}\right) \left(a - b\right)) = (a)^{1}\cdot (a + b)^{1} = a^{2} + a b\]