Compound Integral Expressions.

$a + b + c$ and $a - c$ .

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

$x^{3} - 3 x^{2} + 7$ and $x^{2} - 3$ .

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

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

$x^{2} + 5 x - 10$ and $2 x^{2} + 3 x - 4$ .

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

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

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

$3 a^{2} b^{2} + 2 a b^{3} - 5 a^{3} b$ and $5 a^{2} b^{2} - a b^{3} - b^{4}$ .

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

$a b + a c + c d$ and $a b - a c + c d$ .

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

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

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

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

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

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

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

$2 x^{3} y + 4 x^{2} y^{2} - 8 x y^{3}$ and $2 x y^{3} - 3 x^{2} y^{2} + 5 x^{3} y$ .

89. Division. Polynomials by Monomials.

lint Since a(b + c - d) = ab + ac - ad, ab + ac - ada = aba + aca - ada = b + c - d.

divide a polynomial by a monomial, therefore,

Divide each term of the dividend by the divisor, and add the partial quotients.

Divide $3 a^{4} b^{2} c - 9 a^{3} b c^{2} - 6 a^{2} c^{3}$ by $3 a^{2} c$ .

$\frac{3 a^{4} b^{2} c - 9 a^{3} b c^{2} - 6 a^{2} c^{3}}{3 a^{2} c} & = \frac{3 a^{4} b^{2} c}{3 a^{2} c} - \frac{9 a^{3} b c^{2}}{3 a^{2} c} - \frac{6 a^{2} c^{3}}{3 a^{2} c} & = a^{2} b^{2} - 3 a b c - 2 c^{2} .$