-3 2 -5 3 17 „1 21.1 21 ̊.1 21 the terms with exponents. 1. 1 1 -- 4 1 1.3 2.4) 2.4 1.3.5 2.4.6.8 X =+ 1.3 + X 2.4.6 2.4.6 1.3.5.7 2.4.6.8.10. or aa×(1+5)*. a. a2. 3 the terms and exponents. 1 1 -1 2.4 2.4 2.4.6 2.4.0 4 1.x2 + 2.a 2.4.a2 3.5 the co-efficients. a +(1.+ 2 a Example 5. Expand (a+b)*, or a*× (1+2)* Example 6. Expand into a series (a-b), or ax + .) the answer. 4. 4.8.a2 4.8.12.as 4.8.12.16.a4 Example 7. Expand (a+x)−1, which =a x1+ 2 2.4 3 3.5.7 == + 4 2.4.6.8. the co-efficients. 1.- + 3.5 3 2.4.6 3.5 2.4.6 3.x2 2a 2.4.a2 2.4.6.a3 2.4.6.8.a4 2 Example 10. Expand (a2+x) −1‚a2=b.=(b+x) − § = 1+0)-3 3 5 7 1 3 - + co-efficients. b :(1–; +. - terms 2.a2 PROMISCUOUS EXAMPLES. Example 1. What is the 8th power of (a+b)? 8 7 6 2 5 3 4 4 3 5 2 6 7 8 8 a, a b, a b, a b, a b, a b, a b, ab, b a +8a b+ Ba2b+56 Example 2. What is the 7th power of (a-b)? 1 a = the terms and exponents. 1. 1. 1× 3 -1 &c. = the co-efficients. 1—a+a2 3 = 2 -2 2 - 3 2 -4 3 a .1 a the terms. 1+a+a2 +a3+a* = the terms and co-efficients. -1,-2,-3,-4,-5,-6,-7, &c. the indices. 1.-1.+ -1 -2b-3b2 1.-1.+1.-1 &c. the co-efficients. 1 .1 1 63 a3 = the terms. -1 a 1 (1+0+0+0) h bh Xha ==+: + a Example 5. Expand into a series (a2+b2). By substitution (a2+b2)*= (x+y)1=x1× = (x+y)=a*× (1+2 ) *. = the terms. 1.+11 X the co-efficients, 2 X 2.4 2.x 2.4.x2 2.2 2 2.4 3 y ya + 3.y3 2.4.8.x3 2.a3 8a4 64a6 2a 8a3 Example 6. Expand into a series (a+y) ̄a. Example 7. Expand into a series (c3+x3) (c».+23)*=(a+b)*=a.*. × (1+2) indices. 1.1-1-162. .1 1-363 2 3.6. 3.6. 2.5 =the terms. + —the co-efficients. a3× 3.6.9 Example 9. Find the 5th power of (a2+y3.) (a2+y3)5=(x+y)5. By substitution, x+x+y+x3y2+ x5+5x+y+10x3y2+10x2y3+5x+y= by substitution a10+5a3y3+10a3y®+10a1y9+5a2y12 + 5the answer. y15 Example 10. Find the 4th power of (a+b+x.) (a+b+x)=(a+2)+ by substitution. a++a3%+a2x2+ az3+z1. a2+4a3z+6a2x2+4az3 +z1. a1+4a3(b+x)+ |