An Elementary Treatise On Algebra for the Use of Students in High Schools And C

Thomas Sherwin

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x +y (m-f-w) 2 16. Indicate the 3d power of ) —, ' (p+q) 3 17. Indicate the 4th power of ^it^^TT — - r 3 (c -f- d) 8 18. Indicate the 7th power of . , v, \ 9 : \, , . ■ r 6(r + s) 2 (a + 6-|-c) 3 Art. 107. But if we would have the powers of polynomials in a developed form, they may be obtained by multiplication, in the manner of simple quantities. For example, (m-\-n) 3 =: XXX V1I1. POWERS OF POLYNOMIALS. 171 [m + n) (m -f- n) (m -\- n) = w 3 -f- 3 ?» 2 k -)- 3 « 7^ 2 -|- n 2, and (2bc + d)2=z(...2bc+d)(2bc+d)=z4tb*c2 + To develop the expression a (b -f- c) 2, we must first find the value of (6-j-c) 2, which is 6 2 -f- 2 6 c -|- c 9, and then multiply by a, which gives a b 2 + 2 a 6 c -(- a c 2 . If the multiplication had been performed before raising b -\- c to the second power, the result would have been a 2 6 2 -f- 2 a 2 6 c -f- « 2 c 2, which is errone- cus.
1. Develop (»i — x)K 2. Develoj c(a + 6) 3 .
3. Develop (a+ 6 + c) 2 (m + n).
4. Develop a 3 (x -(- y) 2 .

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