Section 1.3: Algebraic Expressions

  1. Perform the indicated operations and simplify.   solution

    2. (a) \((x+3)(x^2-5x+7)\)   (b) \(\sqrt{x} \left(5x^{3/2}-\dfrac{1}{\sqrt[3]{x}}\right) \)   (c) \((\sqrt{h^3+1}-1)(\sqrt{h^3+1}+1)\)

  2. Expand and simplify.   solution

    3. (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) \((x+2)^{3}\)

  3. Factor the expression.  solution

    4. (a) \(x^2+3x \)   (b) \(2x^3+4x \)   (c) \( x^3-4x \)   (d) \( x^3+9x \)   (e) \(x^2-5x+6 \)   (f) \(x^2-x-6 \)

  4. Factor the expression.   solution

    5. (a) \(2x^2+7x+3 \)   (b) \(5x^2-x-6 \)   (c) \(6x^2+x-1\)   (d) \(3x^2-14x+8 \)

  5. Recognize the type of the expression and use an appropriate method to factor it completely.   solution

    6. (a) \(6x^2y-8xy^2+9xy\)   (b) \(x^2(x^2-9)-25(x^2-9)\)   (c) \(x^3+3x^2-4x-12 \)

  6. Factor the expression completely.  solution

    7. (a) \((z+3)^2-5(z+3)\)   (b)\((y-1)^2+4(y-1)-12 \)   (c) \( x^5y-16xy^5\)