Exam 2: Introduction to Algebra

Divide $12 a b c$ by $0.5 a^{10} b c^{2}$ .

Express without fractions, using negative exponents where needed: $\frac{3 a^{4} b^{-1}}{a^{2} b^{-3}}$

Simplify: $\left(a^{2}\right)^{-5}$

The surface area of a cylinder with radius $r$ and perpendicular height $h$ is given by $2 \pi\left(r^{2}+r h\right)$ . If the radius is increased by 3.00 and the height is doubled, write an expression for the surface area of the new cylinder, and multiply it out.

Square this trinomial: $\left(x^{6}-x^{3} y^{3}+y^{6}\right)$

Divide the polynomial by the monomial: $-a^{3} b^{3}+2 a^{5} b^{3}-3 a^{3} b^{5}$ by $-a^{3} b^{2}$

Combine as indicated, and simplify: $14 x^{2}+2 x+12-4 x+2 x^{2}$

Divide. Write your answer without a negative exponent: $\frac{x^{4}}{x^{-2}}$

Divide: $\frac{a^{5-x}}{a^{3+x}}$

Cube this binomial: $(4 x-3 y)$

Write with positive exponents only: $\left(\frac{2 x y^{3}}{3 z^{2}}\right)^{-3}$

Remove the symbols of grouping (i.e., brackets, braces, parentheses) and collect terms: $-2 c-[(2 a+$ $3 b)-2 b]-[(6 d+b)-3 c]-(10 d+9 a)$

Multiply these binomials, and simplify: $(3 x+2)(x-2 y)(x+y)$

Square this trinomial: $\left(2 x+x y-y^{2}\right)$

Remove the symbols of grouping, and simplify: $\left(2 x-5 y^{2}\right)\left(4 x^{2}+25 y^{4}+10 x y^{2}\right)-\left(2 x-5 y^{2}\right)^{3}$

Write with positive exponents only: $\left(\frac{3 a^{4} b}{5 c^{2} d^{3}}\right)^{-2}$

Write the coefficient of each term. Assume that the letter $x$ is the variable and all other letters are constants. (a) $\frac{a x^{4}}{4}$ (b) $2 a(5 bx^4)$ (c) $\frac{6 b x^{7}}{2 a c}$

Square this trinomial: $\left(y^{8}-2 y^{4}+y^{2}\right)$

Divide the polynomial by the monomial: $-22 p q^{2}+77 p^{3} q^{3}-55 p^{3} q^{5}$ by $-11 q^{2}$

Divide the polynomial by the binomial: $3 a^{2}+5 a+6$ by $a-2$