Exam 2: Introduction to Algebra

Subtract $10\left(x^{2}-y\right)+20$ from $-5-2\left(x^{2}-y\right)$ .

Multiply: $a^{2} \cdot a^{3} \cdot a^{-4}$

Multiply these monomials, and simplify: $\left(4 a^{3}\right)\left(5 a b^{2}\right)\left(a b c^{4}\right)$

Multiply the monomial and binomials, and simplify: $(4 x-5 y)(x+3 y) x$

Remove the symbols of grouping (i.e., brackets, braces, parentheses) and collect terms: 2 - 3[2a- $(5-3 x)]+4(3 x-5)$

Remove the symbols of grouping, and simplify: $[(a-3 b)-(5 a+6 b)][(4 a+b)+(-2 a+3 b)]$

Divide the polynomial by the binomial: $6 a^{2}-6 a-12$ by $6 a-12$

Multiply the polynomial by the monomial, and simplify: $3 a^{2} b\left(a b^{2}-3 a+4 a^{2} b-5 b\right)$

Multiply these polynomials, and simplify: $\left(x^{3}+5 x^{2}-3 x+4\right)\left(4 x^{3}-4 x^{2}+x-1\right)$

Divide $-36 m^{2} p^{3} x$ by $6 m^{2} p x y$ .

Write the coefficient of each term in the expression. Assume that the letter $x$ is the variable and all other letters are constants: $5 a x^{5}+2 x^{2}-k a x$

Add $11 a-b+4 a b, 2 a+13 b-6 a b$ , and $-4 a-8 b+2 a b$ .

Multiply these trinomials, and simplify: $\left(a^{2}+3 a b-9 b\right)\left(a-3 a b-b^{2}\right)$

The volume of a cylinder of radius $3 r$ and perpendicular height $4 r$ is given by $\pi(3 r)^{2}(4 r)$ . Simplify this expression.

Remove the symbols of grouping (i.e., brackets, braces, parentheses) and collect terms: $2(5 x-2)-3$

Divide the polynomial by the binomial: $6 x^{2}+2 x-10$ by $-3 x+2$

Evaluate: $\frac{7 a^{2}}{b^{0}}$

Combine as indicated, and simplify: $-5 a+5 a+b+6 b$

Subtract $5 a-12 b-3 c$ from $10 b-6 c+4 d$ .

Multiply these binomials, and simplify: $\left(y^{2}+13\right)\left(y^{3}-2\right)$