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nydus/The First Steps in AlgebraPublic

This textbook introduces the fundamental concepts of algebra, including definitions of units, quantities, and number symbols. It explains the use of letters to represent numbers and outlines the signs for basic mathematical operations.

Page 184 of 227

Table of Contents

Cube Roots of Compound Expressions.

$3 x^{3} - 2 x^{2} + 1$ .

$3 c^{2} + 24 c - 12$ .

$2 b^{4}$ .

$10 - 16 x - 39 x^{2} + 2 x^{3} + 15 x^{4}$ .

$a^{4} - a x^{3} + x^{4}$ .

$(a - b) x^{3} + (b + c) x^{2} - (c + 1) x$ .

$(a + b) x^{4} - (a - b) x^{3} - (c + 2) x$ .

$(a + 1) x^{3} - (b + c) x^{2} + (b - c) x$ .

[2]Exercise26.

$m^{2} + 2 m n + n^{2}$ .

$c^{2} - 2 a c + a^{2}$ .

$a^{2} + 4 a c + 4 c^{2}$

$9 a^{2} - 12 a b + 4 b^{2}$ .

$4 a^{2} + 12 a b + 9 b^{2}$ .

$a^{2} - 6 a b + 9 b^{2}$ .

$4 x^{2} - 4 x y + y^{2}$ .

$y^{2} - 4 x y + 4 x^{2}$ .

$a^{2} + 10 a b + 25 b^{2}$ .

$4 a 2 - 20 a c + 25 c^{2}$ .

$x^{2} - y^{2}$ .

$16 a^{2} - b^{2}$ .

$4 b^{2} - 9 c^{2}$ .

$x^{2} + 10 b x + 25 b^{2}$ .

$y^{2} - 4 y z + 4 z^{2}$ .

$y^{2} - 9 z^{2}$ .

$4 a^{2} - 9 b^{2}$ .

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