Compound Integral Expressions.

descending powers of a . l * 8 c r a 2 & − & a b & − & a c & + & b 2 & − & b c & + & c 2 a & + & b & + & c \cline 1 − 11 a 3 & − & a 2 b & − & a 2 c & + & a b 2 & − & a b c & + & a c 2 & + & a 2 b & & & − & a b 2 & − & a b c & & & + & b 3 & − & b 2 c + b c 2 & & & + & a 2 c & & & − & a b c & − & a c 2 & & & + & b 2 c − b c 2 & + & c 3 \hline a 3 & & & & & & & − & 3 a b c & & & + & b 3 & & & + & c 3

The pupil should observe that, with a view to bringing like terms of the partial products in columns, the terms of the multiplicand and multiplier are arranged in the same order.

Exercise 22.

Find the product of:

$x + 7$ and $x + 6$ .

$x - 7$ and $x + 6$ .

$x + 7$ and $x - 6$ .

$x - 7$ and $x - 6$ .

$x + 8$ and $x - 5$ .

$2 x + 3$ and $2 x + 3$ .

$2 x - 3$ and $2 x - 3$ .

$2 x + 3$ and $2 x - 3$ .

$3 x - 2$ and $2 - 3 x$ .

$5 x - 3$ and $4 x - 7$ .

$a - 2 b$ and $a + 3 b$ .

$a - 7 b$ and $a - 5 b$ .

$5 x - 3 y$ and $5 x - 3 y$ .

$x - b$ and $x - c$ .

$2 m - p$ and $4 m - 3 p$ .