Ejercicios Resueltos de Productos Notables

a)  $(b^n+2)(b^n+3)$→$(b^n)^2+(+2+3)b^n+(+2)(+3)$
→$b^{2n}+5b^n+6\bullet$

b)  $(3a^5+\frac{1}{3}a)^2$→$(3a^5)^2+2(3a^5)\frac{1}{3}a+(\frac{1}{3}a)^2$
→$9a^{10}+2a^6+\frac{1}{9}a^2\bullet$

c)  $(ax^{2m}-x^m)^2$→$(ax^{2m})^2-2.ax^{2m}.x^m+(x^m)^2$
→$a^2x^{4m}-2ax^{3m}+x^{2m}\bullet$

d)  $(2x-\frac{5}{3})(2x-\frac{4}{5})$→$(2x)^2+(-\frac{5}{3}-\frac{4}{5})2x+(-\frac{5}{3})(-\frac{4}{5})$
→$4x^2-\frac{74}{15}x+\frac{4}{3}\bullet$

e)  $(\frac{3}{4}xy-ab)(\frac{3}{4}xy+ab)$→$(\frac{3}{4}xy)^2-(ab)^2$
→$\frac{9}{16}x^2y^2-a^2b^2\bullet$

f)  $(ab^2-2b)^3$→$(ab^2)^3-3(ab^2)^2(2b)+3(ab^2)(2b)^2-(2b)^3$
→$a^3b^6-6a^2b^5+12ab^4-8b^3\bullet$