Exam 2: Introduction to Algebra

Divide $7x^8y^2z^3 by wxyz^4$ .

Express without fractions, using negative exponents where needed: $\frac{2}{a}$

Multiply these binomials, and simplify: $\left(2 a^{2} b^{3}-8 m n^{2}\right)\left(a^{2} b^{3}+3 m n^{2}\right)$

A simply-supported beam has a uniformly-distributed load. The deflection at the point $x$ metres from the left end of the beam is given by $y=\frac{\omega}{24 k}\left(L^{3} x-2 L x^{3}+x^{4}\right)$ where $L$ is the length of the beam in metres, $\omega$ is the load in $\mathrm{N} / \mathrm{m}$ , and $k$ is a constant. What is the coefficient of $x$ for a 2.00 -metre beam if the load is $600\overline{0} \mathrm{~N} / \mathrm{m}$ and $k$ is $4.00 \times 10^{7}$ ?

Multiply: $\mathrm{c}^{\mathrm{x}+4} \cdot \mathrm{c}^{\mathrm{x}+5}$

Remove the symbols of grouping (i.e., brackets, braces, parentheses) and collect terms: $5 p+8 q-4 r-$ $(9 q+6 r)+(30 p-9 q)$

Find the sum of $4 x+9 p-5 y,-3 p+2 p+3 x$ , and $-4 y+7 p-9 y$ .

Raise to the power indicated: $\left(4 y^{6}\right)^{-2}$

Simplify: $\left(7^{4}\right)^{x+2}$

Remove the symbols of grouping (i.e., brackets, braces, parentheses) and collect terms: $21 a^{2}+2 b^{2}-$ $6\left(a b+3 a^{2}-5 b^{2}\right)$

Square this binomial: $(x-y)$

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

State the degree of each expression. (a) $3 x^{4}+4 y^{6}$ (b) $7 x^{2}+3 x-5$ (c) $-9 x y^{2}+4 y^{3}$

Evaluate: $\left(3 x-4 y^{2}\right)^{0}$

Divide the polynomial by the trinomial: $x^{3}+3 x^{2}+5 x$ by $x^{2}+3 x+1$

Write the coefficient of each term in the expression: $4 x^{4}-6(2 x)$

Divide $16 a^{2} b$ by $4 a b$ .

The density of a block is given by $\frac{7.20}{(3 x)(2 x)^{2}} \mathrm{~g} / \mathrm{cm}^{3}$ . Express the density without fractions, using negative exponents where needed.

Find the sum of $5-x^{2}+3 m, 5 x+9-2 x^{2}, 9 m+7+3 x^{2}-x$ , and $15 x^{3}+2 x^{2}-5$ .

Remove the symbols of grouping, and simplify: $(2 x+3)\left(4 x^{2}-6 y+9\right)-(2 x-3)\left(4 x^{2}+6 y+9\right)$