Beginning Algebra
Simplify: (−4)2×(−4)3×z5×z−2\(\left\)(-4\(\right\))^2\(\times\]\left\)(-4\(\right\))^3\(\times\) z^5\(\times\) z^{-2}
Solve for xx:
2x23=8\(\frac{2^{x}\)}{2^3}=8
Simplify (3x2)3⋅(3x)2(3x^2)^3 · (3x)^2 completely.
Given the equation (2x5y)3=16125(\(\frac{2x}{5y}\))^3 = \(\frac{16}{125}\) with xx and yy nonzero, find xy\(\frac{x}{y}\).
Simplify the rational expression 3x−2y3x−5y−1\(\displaystyle\]\frac{3x^{-2}\)y^3}{x^{-5}y^{-1}} and express your answer with only positive exponents.
Simplify (x3y5x6y2)−1\(\left\)(\(\frac{x^3y^5}{x^6y^2}\]\right\))^{-1}.
Determine the degree of the polynomial P(x,y)=x4+2x2y3+y6P(x,y) = x^4 + 2x^2 y^3 + y^6 and justify how you found it.
Simplify (4x2+6x)+(−x2+2x)(4x^2 + 6x) + (-x^2 + 2x) and factor the result by pulling out the greatest common factor.
Expand and simplify fully: (x + 2)(x + 3)(x + 4). Show the final cubic polynomial.
Expand (3x2+4)2(3x^2 + 4)^2.
Factor completely by extracting the GCF: 14x3−21x2+35x14x^3-21x^2+35x
Factor x2+11x+24x^2 + 11x + 24.
Factor by trial-and-error: 12x2+7x−1012x^2 + 7x - 10
Given the polynomial 125z3−8125z^3-8, factor completely.
Use the quadratic formula to solve for: (x+2)(x+5)−14=0(x + 2)(x + 5) - 14 = 0.
Simplify the rational expression x2−9x2−6x+9\(\frac{x^2-9}{x^2-6x+9}\) and state any domain restrictions.
Simplify the multi-step expression to lowest terms: (2x3y÷4x29y3)⋅27y8x\(\displaystyle\) \(\left\)( \(\frac{2x}{3y}\) \(\div\) \(\frac{4x^2}{9y^3}\) \(\right\)) \(\cdot\) \(\frac{27y}{8x}\)
