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Flashcards · Maths · Algebra

Simplifying and Expanding Expressions

17 cards

  1. What is the difference between an expression and an equation?

    An expression has no equals sign, such as \(3x + 5\). An equation has one and can be solved, such as \(3x + 5 = 20\).

  2. What is an identity?

    An equation that is true for every value of the letter, written with \(\equiv\), such as \(2(x + 3) \equiv 2x + 6\).

  3. What are like terms?

    Terms with the same letters to the same powers. \(3x\) and \(5x\) are like terms, but \(3x\) and \(3x^2\) are not.

  4. Simplify \(4a + 3b - a + 5b\).

    \(3a + 8b\).

  5. What is \(3x \times 4x^2\)?

    \(12x^3\). Multiply the numbers and add the powers.

  6. What is \(12x^5 \div 3x^2\)?

    \(4x^3\). Divide the numbers and subtract the powers.

  7. Expand \(3(2x - 5)\).

    \(6x - 15\).

  8. Expand \(-2(x - 4)\).

    \(-2x + 8\), because a negative times a negative is a positive.

  9. What does expanding two brackets involve?

    Multiplying every term in one bracket by every term in the other, which gives four products to collect.

  10. Expand and simplify \((x + 3)(x + 5)\).

    \(x^2 + 8x + 15\).

  11. Expand and simplify \((x + 7)(x - 4)\).

    \(x^2 + 3x - 28\).

  12. Expand and simplify \((x + 3)(x - 3)\).

    \(x^2 - 9\). The middle terms cancel.

  13. What is the common mistake with \((x + 3)^2\)?

    Writing \(x^2 + 9\). It is \((x + 3)(x + 3) = x^2 + 6x + 9\), and the middle term is the one people miss.

  14. Expand and simplify \((x - 4)^2\).

    \(x^2 - 8x + 16\).

  15. How can you check an expansion?

    Put a number such as \(x = 1\) into the original and your answer. They must give the same value.

  16. How do you write an even number and an odd number using \(n\)?

    Even: \(2n\). Odd: \(2n + 1\).

  17. How do you show that the sum of two consecutive integers is odd?

    \(n + (n + 1) = 2n + 1\), which is always odd.