Exercise
$\left(\frac{1}{5}a^{n-1}b^n-\frac{1}{4}a^n\right)^4$
Step-by-step Solution
Learn how to solve special products problems step by step online. Expand the expression (1/5a^(n-1)b^n-1/4a^n)^4. Expand the binomial \left(\frac{1}{5}a^{\left(n-1\right)}b^n-\frac{1}{4}a^n\right)^4. The power of a product is equal to the product of it's factors raised to the same power. The power of a product is equal to the product of it's factors raised to the same power. Multiply the fraction and term in - \left(\frac{1}{125}\right)a^{3\left(n-1\right)}b^{3n}a^n.
Expand the expression (1/5a^(n-1)b^n-1/4a^n)^4
Final answer to the exercise
$\frac{1}{625}a^{\left(4n-4\right)}b^{4n}-\frac{1}{125}a^{\left(4n-3\right)}b^{3n}+\frac{6}{25}a^{\left(2n-2\right)}b^{2n}\left(-\frac{1}{4}a^n\right)^2+\frac{4}{5}a^{\left(n-1\right)}b^n\left(-\frac{1}{4}a^n\right)^3+\left(-\frac{1}{4}a^n\right)^4$