Simplify the following.

(-x^2+2x + 7)+(2x^2-7x -7)

Simplify the following.

(2m^2-mn + 4n^2)-(5m^2-n^2)+(7m^2 -2mn)

Expand and simplify.

2(12a -5)(3a - 7)

Expand and simplify.

(2x^2y - 3xy^2)(4xy^2+5x^2y)

Expand and simplify.

(4x -1)(5x + 2)(x -3)

Expand and simplify.

(3p^2+ p - 2)^2

Is there a value of a such that f(x) = 9x^2 + 4 and g(x) = (3x - a)^2 are equivalent? Explain.

If Benny is away from Candy for n consecutive days, then the amount of heartache Candy feels is given by h(n) = (2n + 1)^3.

a) If Bonnie is absent, by how much does Candy’s pain increase between day n and day n + 1?

b) How much more pain will he feel on day 6 than on day 5?

Factor

3m(m- 1) + 2m(1 - m)

Factor

x^2 -27x + 72

Factor

15x^2 -7xy -2y^2

Factor

(2x - y + 1)^2-(x-y-2)^2

Factor

5xy - 10x -3y + 6

Factor

p^2 -m^2 + 6m -9

Use factoring to determine the x-intercepts of the curve

y =x^3 -4x^2-x + 4

Simplify. State any restrictions on the variables.

\frac{4a^2b}{5ab^3} \div \frac{6a^2b}{35ab}

Simplify. State any restrictions on the variables.

\displaystyle \frac{x -2}{x^2-x -12} \times \frac{2x - 8}{x^2-4x + 4}

Simplify. State any restrictions on the variables.

\displaystyle \frac{5}{t^2-7t - 18} + \frac{6}{t + 2}

Simplify. State any restrictions on the variables.

\displaystyle \frac{4x}{6x^2 + 13x + 6} - \frac{3x}{4x^2 -9}

Miruo found that two rational functions each simplified to f(x) = \frac{2}{x + 1}.

Are Miruo's two rational functions equivalent? Explain.

Roman thinks that he has found a simple method for determining the sum of the reciprocals of any three consecutive natural numbers. He writes, for example,

\displaystyle \frac{1}{3} + \frac{1}{4} + \frac{1}{5} = \frac{47}{60}, \frac{1}{4} + \frac{1}{5} + \frac{1}{6} = \frac{74}{120}, or \displaystyle \frac{37}{60}

Roman conjectures that before simplification, the numerator of the sum is three times the product of the first and third denominators, plus 2. Also, the denominator of the sum is the product of the three denominators. Is Roman’s conjecture true?