Question

​then (x/y)^3 + (x/y)^6

Answer 1

Answer:

→Use Division Distributive Property: $\tt{(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}$

$\tt\red{\implies\frac{{x}^{6}}{{y}^{6}}+{(\frac{x}{y})}^{3}}$

→Use Division Distributive Property: $\tt{(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}$

$\sf\blue{\implies\frac{{x}^{6}}{{y}^{6}}+\frac{{x}^{3}}{{y}^{3}}}$

→ Rewrite the expression with a common denominator.

$\tt\pink{\implies\frac{{x}^{6}+{x}^{3}{y}^{3}}{{y}^{6}}}$

→4 Factor out the common term $\tt{x}^{3}$

.

$\tt\green{\implies\frac{{x}^{3}({x}^{3}+{y}^{3})}{{y}^{6}}}$

→ Use Sum of Cubes: $\tt{a}^{3}+{b}^{3}=(a+b)({a}^{2}-ab+{b}^{2})$

$\tt\blue{\implies\frac{{x}^{3}((x+y)({x}^{2}-(x)(y)+{y}^{2}))}{{y}^{6}}}$

→ Remove parentheses.

$\red{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\tt\orange{\implies\frac{{x}^{3}(x+y)({x}^{2}-xy+{y}^{2})}{{y}^{6}}}}}}}}}}}$