Elementary Algebra : Embracing the First Principles of the Science

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What is the square of the binomial a + 11 Ans. a* + 2a + 1, 6. What is the square of the binomial a — 1 ?
Ans. a= — 2a + 1, 7. What is the cube of 9a — 36 ?
Ans. 729o3 - 7290=5 + 24306" — 276'.
8. What is the third power of a — 1 ?
Ans, a' — So" + 3a - 1.
or POWERS. 149 9 What is the 4th power of x — yl Am. X* — Ax^y + Ga^y^ — 4a;y' -}- y*.
10 What is the cuhe of the trinomial a; + y + z ?
Answer.
x'+3x'y+3x''z+3xy^+3xz'+3y^2+3yz'+Gxyz+y3+z^ 1 1 . What is the cube of the trinomial Ha' — 4ab + 3
...6^ 1 Answer.
Ha — 4Sa^b + I32a*b^ — 208a^3+ IGSa^S*— 108a6*+275« To raise a fracfion to any power.
83. A power of a fraction is obtained by multiplyipg the fraction by itself a certain number of times ; that is, by multiplying the numerator by the numerator, and the deno- minator by the denominator.
a Thus, the cube of -^ which is written 6 [t) -t a a a?
is found by cubing the numerator and denominator sepa- rately.
2. What is the square of the fraction -; 1 b + e We have i a — e y_{a—cY_ a^ — ^ac + y.


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