Algebraic Expressions and Formulas eLearn.Punjab Solutions
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Questions and Answers

What is the result of $(a + b)^2 - (a - b)^2$?

  • $4ab$ (correct)
  • $2(a^2 + b^2)$
  • $4a^2 - 4b^2$
  • $2(2a^2 - 2b^2)$
  • Given that $a + b + c = 7$ and $ab + bc + ca = 12$, what is the value of $a^2 + b^2 + c^2$?

  • $31$ (correct)
  • $37$
  • $25$
  • $49$
  • What is the product of $(x + y)(x - y)(x^2 + xy + y^2)(x^2 - xy + y^2)$?

  • $x^8 - y^8$
  • $x^6 - y^6$ (correct)
  • $x^2 - y^2$
  • $x^4 - y^4$
  • When $a + b = 5$ and $a - b = 3$, what is the value of $a^2 + b^2$?

    <p>$25$</p> Signup and view all the answers

    What is the sum of all possible values of $x$ that satisfy $x^2 - 7x + 12 = 0$?

    <p>$7$</p> Signup and view all the answers

    If $ab + bc + ca = 30$ and $a + b + c = 10$, what is the value of $abc$?

    <p>$50$</p> Signup and view all the answers

    In the expression 3x^2y + 6, when x = -4 and y = 9, what is the value of the expression 5(x + y)?

    <p>25</p> Signup and view all the answers

    For the expression (8x^2 + 8)(2x + 2), evaluate the expression when x = 5.

    <p>120</p> Signup and view all the answers

    For the expression x^3y - 2z, what is the value of the expression when x = 3, y = -1, and z = -2?

    <p>-10</p> Signup and view all the answers

    In the expression 3x + 8 / 2x - 1, what is the simplified form of the expression?

    <p>1.5x + 4</p> Signup and view all the answers

    Reduce the rational expression (x^3 - y^3) / (x^2 - 2xy + y^2) to lowest form.

    <p>x^2 - y^2</p> Signup and view all the answers

    For the expression x - 1 / (x^2 - 1), what is the simplified form of the expression?

    <p>1 / (x + 1)</p> Signup and view all the answers

    What is the value of x in the equation x^3 + 3 = 512, given x + 1 = 8?

    <p>7</p> Signup and view all the answers

    What is the factorization of 125x^3 - 1331y^3?

    <p>(5x - 11y) (25x^2 + 55xy + 121y^2)</p> Signup and view all the answers

    What is the product of (x - 1) and x^2 - 2x + 1, where x = 4?

    <p>468</p> Signup and view all the answers

    What is the factorization of 64x^3 + 343y^3?

    <p>(4x + 7y) (16x^2 - 28xy + 49y^2)</p> Signup and view all the answers

    If x = 4, what is the value of (x + 1)^3 + 2?

    <p>514</p> Signup and view all the answers

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