Integral Compound Expressions.

2 b − 6 a b 2 − b 3 ; 3 a 2 b + 4 a b 2 .

$a^{3} - 2 a^{2} b - 2 a b^{2}$ ; $a^{2} b - 3 a b^{2} - b^{3}$ ; $3 a b^{2} - 2 a^{3} - b^{3}$ .

$7 x^{3} - 2 x^{2} y + 9 x y^{2} + 13 y^{3}$ ; $5 x^{2} y - 4 x y^{2} - 2 x^{3} - 3 y^{3}$ ; $y^{3} - x^{3} - 3 x^{2} y - 5 x y^{2}$ ; $2 x^{2} y - 5 y^{3} - 2 x^{3} - x y^{2}$ .

Show that $x + y + z = 0$ , if $x = a - b - c$ , $y = 2 b + 2 c - 3 a$ , and $z = 2 a - b - c$ .

Show that $x + y = 3 z$ , if $x = 3 a^{2} - 6 a + 12$ , $y = 9 a^{2} + 12 a - 21$ , and $z = 4 a^{2} + 2 a - 3$ .

83. Subtraction of Integral Compound Expressions.

The subtraction of one expression from another, if none of the terms are alike, can be represented only by connecting the subtrahend with the minuend by means of the sign $-$ .

If, for example, it is required to subtract $a + b + c$ from $m + n - p$ , the result will be represented by $m + n - p - (a + b + c);$ or, removing the parenthesis (§ 38), $m + n - p - a - b - c .$

If, however, some of the terms in the two expressions are alike, we can replace two like terms by a single term.

Thus, suppose it is required to subtract $a^{3} + 2 a^{2} + 3 a - 5$ from $2 a^{3} - 3 a^{2} + 2 a - 1$ ; the result may be expressed as follows: $2 a^{3} - 3 a^{2} + 2 a - 1 - (a^{3} + 2 a^{2} + 3 a - 5);$ or, removing the parenthesis (§ 38),