Page:Elementary algebra (1896).djvu/193

Performing the operations indicated, we have

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

Note. 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. $\left({\frac {a^{2}b}{3}}-{\frac {c^{2}}{4}}\right)^{5}.$ 11 $\left({\frac {2abc}{3}}-{\frac {2d^{2}}{5}}\right)^{4}.$ 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 •