Page:Elementary algebra (1896).djvu/193

Rh Performing the operations indicated, we have

$$\begin{align} a^3+6a^2b-3a^2c+12ab-12abc+3ac^2+8b^3 & -12b^2c \\ & + 6 bc^2-c^3 \\ \end{align} $$

A full discussion of the Binomial Theorem for Positive Integral Index is given in Chapter XXXVII.

EXAMPLES XX. e. Expand the following expressions:

1. $${\left ( x+y \right )}^5.$$ 2. $${\left ( a-b \right )}^5.$$ 3. $$(2a+b6)^6.$$ 4. $$(3x+2y)^5.$$ 5. $$(2x-3b)^5.$$ 6. $$(c^2 + d^2).$$ 7. $$(2ab-c^2)^5.$$ 8. $$(3a^2 b^2-2cd^3)^5.$$ 9. $$(\frac{1}{2}x^2 + z^3)^5.$$ 10. $$\left ( \frac{a^2b}{3} - \frac{c^2}{4} \right ) ^5 .$$ 11 $$\left ( \frac{2 abc}{3} - \frac{2d^2}{5} \right ) ^4.$$ 12. $$\left( \frac{2a}{x}-\frac{b^2}{z} \right )$$ 13. (a + 2b + 3c)^3. 14. (a-b-c)^3. 15. (2a - \frac{b}{2}-c^2)^3. 16. (a + &-2c)4. 17. {a + h + c- ay. 18. (a + 2 64 c-2f?)3. 19. (« _2 6 + c-(^)4. 20. Find the middle term of (a + l)io. 21. Find the two middle terms of {x — ?/)ii. 22. Find the term independent of a in ( — - — J •