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nydus/The First Steps in AlgebraPublic

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Table of Contents

VIII.

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

The highest common factor in Algebra corresponds to the greatest common measure, or greatest common divisor in Arithmetic. We cannot apply the terms greatest and least to an algebraic expression in which particular values have not been given to the letters contained in the expression. Thus $a$ is greater than $a^{2}$ , if $a$ stands for $\frac{1}{4}$ .

Exercise 40.

Find the H. C. F. of:

$330$ and $546$ .

$20 x^{3}$ and $15 x^{4}$ .

$42 a x^{2}$ and $60 a^{2} x$ .

$35 a^{2} b^{2}$ and $49 a b^{3}$ .

$28 x^{4}$ and $63 y^{4}$ .

$54 a^{2} b^{2}$ and $56 a^{3} b^{3}$ .

$x^{3} + 3 x^{2} y$ and $x^{3} + 27 y^{3}$ .

$x^{2} + 3 x$ and $x^{2} - 9$ .

$2 a x^{3} + x^{3}$ and $8 a^{3} + 1$ .

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

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

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

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

$x^{2} + 5 x + 6$ and $x^{2} + 4 x + 3$ .

$x^{2} - 9 x + 18$ and $x^{2} - 10 x + 24$ .

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

$x^{2} - 3 x + 2$ and $x^{2} - 4 x + 3$ .

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

$x^{2} - 4 x - 5$ and $x^{2} - 25$ .

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

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