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nydus/The First Steps in AlgebraPublic

Page 93 of 227

Table of Contents

VIII.

Find the product of all the different factors, taking each factor the greatest number of times it occurs in any of the given expressions.

Exercise 41.

Find the L. C. M. of:

$9 x y^{3}$ and $6 x^{2} y$ .

$3 a b c^{2}$ and $2 a^{2} b c^{3}$ .

$4 a^{3} b$ and $10 a b^{3}$ .

$6 a^{3} b^{3}$ and $15 a^{2} b^{4}$ .

$21 x y^{3}$ and $27 x^{3} y^{5}$ .

$x y^{3} z^{2}$ and $x^{2} y^{2} z^{3}$ .

$a^{2}$ and $a^{2} + a$ .

$x^{2}$ and $x^{3} - 3 x^{2}$ .

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

$x^{2} - 1$ and $x^{2} - x$ .

$x^{2} + x y$ and $x y + y^{2}$ .

$x^{2} + 2 x$ and $(x + 2)^{2}$ .

$a^{2} + 4 a + 4$ and $a^{2} + 5 a + 6$ .

$c^{2} + c - 20$ and $c^{2} - c - 30$ .

$b^{2} + b - 42$ and $b^{2} - 11 b + 30$ .

$y^{2} - 10 y + 24$ and $y^{2} + y - 20$ .

$z^{2} + 2 z - 35$ and $z^{2} - 11 z + 30$ .

$x^{2} - 64; x^{3} - 64$ ; and $x + 8$ .

$a^{2} - b^{2}; (a + b)^{2}$ ; and $(a - b)^{2}$ .

$4 a b (a + b)^{2}$ and $2 a^{2} (a^{2} - b^{2})$ .

$y^{2} + 7 y + 12; y^{2} + 6 y + 8$ ; and $y^{2} + 5 y + 6$ .

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

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

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