Some Algebra Practice questions
Evaluate each expression without using a calculator. solution
(a) \((-3)^{4}\) (b) \(-3^{4}\) (c) \(3^{-4}\) (d) \(\frac{5^{23}}{5^{21}}\) (e) \(\left(\frac{2}{3}\right)^{-2}\) (f) \(16^{-3 / 4}\)
Simplify each expression. Write your answer without negative exponents. solution
(a) \(\sqrt{200}-\sqrt{32}\) (b) \(\left(3 a^{3} b^{3}\right)\left(4 a b^{2}\right)^{2}\)
(c) \(\left(\dfrac{3 x^{3 / 2} y^{3}}{x^{2} y^{-1 / 2}}\right)^{-2}\)
Expand and simplify. solution
(a) \(3(x+6)+4(2 x-5)\) (b) \((x+3)(4 x-5)\) (c) \((\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b})\)
(d) \((2 x+3)^{2}\) (e) \((x+2)^{3}\)
Factor the expression. solution
(a) \(x^2+3x \) (b) \(2x^3+4x \) (c) \( x^3-4x \) (d) \( x^3+9x \) (e) \(x^2-5x+6 \) (f) \(x^2-x-6 \)
Factor the expression. solution
(a) \(x^2+7x+3 \) (b) \(x^2-x-6 \) (c) \(6x^2+x-1\) (d) \(3x^2-14x+8 \)
Simplify the rational expression. solution
(a) \(\dfrac{x^{2}+3 x+2}{x^{2}-x-2}\) (b) \(\dfrac{2 x^{2}-x-1}{x^{2}-9} \cdot \dfrac{x+3}{2 x+1}\)
(c) \(\dfrac{\frac{y}{x}-\frac{x}{y}}{\frac{1}{y}-\frac{1}{x}}\)
(a) \(\dfrac{x^3-9x}{2x-6} \) (b) \(\dfrac{\frac{1}{2+h}-\frac{1}{2}}{h} \) (c) \(\displaystyle{ \frac{(5+h)^2-25}{h}} \)