Exam 2: Introduction to Algebra

How many terms are in the following expression? $(-3 x) 12 y+y^{4}-12 x(-2 y)+x y$

Remove the symbols of grouping, and simplify: $\left(2 x+3 y z^{2}\right)^{2}+\left(2 x-3 y z^{2}\right)^{2}-2\left(4 x^{2}+15 y^{2} z^{4}\right)$

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

Cube this binomial: $(x+5 y z)$

Multiply these binomials, and simplify: $\left(7 a b^{2}+3 b^{2}\right)\left(2 a b^{3}-5 a^{2}\right)$

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

Divide the polynomial by the binomial: $14 x^{2}+5 x-11$ by $-2 x+1$

Multiply these polynomials, and simplify: $\left(5 m^{2}+2-3 m\right)\left(6 m^{3}-4 m^{2}+4+2 m\right)$

Divide the polynomial by the monomial: $15 m^{2} n p+45 m n p^{2}-35 m^{2} n^{2} p^{2}$ by $-5 m n p$

Divide $-12 p^{3} w^{4} z$ by $-4 p^{3} w$ .

How many terms are in the following expression? $\frac{3}{4}(x-2)-\frac{1}{3}\left(x^{2}+3\right)$

Divide $(x + 3y)^3 by (x + 3y)^2$ .

Divide the polynomial by the trinomial: $16 x^{4}+12 x^{2}+4 x+60$ by $x^{2}+2 x+1$

Combine as indicated, and simplify: $3 x-4 x+2 y-4 y$

Multiply the binomial and trinomial, and simplify: $(c-d)\left(c^{2}-2 c d+d^{2}\right)$

Multiply: $x \cdot x^{3}$

Divide. Write your answer without a negative exponent: $\frac{4^{10}}{4^{6}}$

Multiply these polynomials, and simplify: $\left[x^{2}-2 x(y+z)+(y+z)^{2}\right](y+z)$

Divide the polynomial by the monomial: $25 x^{3} y-5 x y^{3}-15 x^{2}+20 y^{3}$ by $5 x^{2} y^{2}$

Divide the polynomial by the monomial: $m-m^{2} n-m n^{2}$ by $-m$