Equivalent Expressions practice questions

Equivalent Expressions questions

Pick an answer before you look. Tapping a choice shows which one was right and opens the worked explanation, and a miss is remembered so Weak Skills can replay that skill. It stays in this browser.

1. 1Equivalent expressionsFoundation

   Which expression is equivalent to 3(x + 2) - 2?Which expression is equivalent to 3(x + 2) - 2?

   • A3x + 43x + 4
   • B3x - 43x - 4
   • Cx + 4x + 4
   • D3x + 63x + 6
   Show the answer and explanationHide the explanation

   Answer: 3x + 43x + 4

   Distribute first, then collect: 3(x + 2) = 3x + 6, and 3x + 6 - 2 = 3x + 4. The usual slip is distributing to the first term only and leaving 3x + 2 - 2.Distribute first, then collect: 3(x + 2) = 3x + 6, and 3x + 6 - 2 = 3x + 4. The usual slip is distributing to the first term only and leaving 3x + 2 - 2.

   How did you do?Got itMissed it
2. 2Equivalent expressionsFoundation

   Which expression is equivalent to (x + 7)(x - 2)?Which expression is equivalent to (x + 7)(x - 2)?

   • Ax² - 5x - 14x^2 - 5x - 14
   • Bx² + 5x - 14x^2 + 5x - 14
   • Cx² + 5x + 14x^2 + 5x + 14
   • Dx² - 14x^2 - 14
   Show the answer and explanationHide the explanation

   Answer: x² + 5x - 14x^2 + 5x - 14

   Multiplying out: x² - 2x + 7x - 14 = x² + 5x - 14. The middle term comes from adding -2 and 7, and forgetting it entirely gives x² - 14.Multiplying out: x^2 - 2x + 7x - 14 = x^2 + 5x - 14. The middle term comes from adding -2 and 7, and forgetting it entirely gives x^2 - 14.

   How did you do?Got itMissed it
3. 3Equivalent expressionsFoundation

   Which expression is equivalent to (x - 6)(x + 6)?Which expression is equivalent to (x - 6)(x + 6)?

   • Ax² + 36x^2 + 36
   • Bx² - 12x - 36x^2 - 12x - 36
   • Cx² - 12x + 36x^2 - 12x + 36
   • Dx² - 36x^2 - 36
   Show the answer and explanationHide the explanation

   Answer: x² - 36x^2 - 36

   The middle terms cancel because the constants are opposites: -6x + 6x = 0. This is the difference of squares, and recognizing it saves expanding every time.The middle terms cancel because the constants are opposites: -6x + 6x = 0. This is the difference of squares, and recognizing it saves expanding every time.

   How did you do?Got itMissed it
4. 4Equivalent expressionsFoundation

   Which expression is equivalent to (x - 4)(x + 9)?Which expression is equivalent to (x - 4)(x + 9)?

   • Ax² - 5x - 36x^2 - 5x - 36
   • Bx² + 5x + 36x^2 + 5x + 36
   • Cx² - 36x^2 - 36
   • Dx² + 5x - 36x^2 + 5x - 36
   Show the answer and explanationHide the explanation

   Answer: x² + 5x - 36x^2 + 5x - 36

   The middle term comes from -4 and +9, which add to +5; the constant is their product, -36. Forgetting the middle term entirely gives x² - 36.The middle term comes from -4 and +9, which add to +5; the constant is their product, -36. Forgetting the middle term entirely gives x^2 - 36.

   How did you do?Got itMissed it
5. 5Equivalent expressionsStandard

   If 3a + 2b = 12, which expression gives a in terms of b?If 3a + 2b = 12, which expression gives a in terms of b?

   • A12 + 2b3(12 + 2b)/3
   • B12 - 2b12 - 2b
   • C12 - 2b3(12 - 2b)/3
   • D2b - 123(2b - 12)/3
   Show the answer and explanationHide the explanation

   Answer: 12 - 2b3(12 - 2b)/3

   Subtract 2b from both sides to get 3a = 12 - 2b, then divide both sides by 3.Subtract 2b from both sides to get 3a = 12 - 2b, then divide both sides by 3.

   How did you do?Got itMissed it
6. 6Equivalent expressionsStandard

   Which expression is equivalent to (3x - 5)(3x + 5)?Which expression is equivalent to (3x - 5)(3x + 5)?

   • A3x² - 253x^2 - 25
   • B9x² + 259x^2 + 25
   • C9x² - 30x - 259x^2 - 30x - 25
   • D9x² - 259x^2 - 25
   Show the answer and explanationHide the explanation

   Answer: 9x² - 259x^2 - 25

   This is a difference of squares: (a - b)(a + b) = a² - b², with a = 3x and b = 5, giving 9x² - 25.This is a difference of squares: (a - b)(a + b) = a^2 - b^2, with a = 3x and b = 5, giving 9x^2 - 25.

   How did you do?Got itMissed it
7. 7Equivalent expressionsStandard

   Which expression is equivalent to 2(x - 3) - 3(2x + 1)?Which expression is equivalent to 2(x - 3) - 3(2x + 1)?

   • A-4x - 9-4x - 9
   • B-4x + 9-4x + 9
   • C8x - 98x - 9
   • D-4x - 3-4x - 3
   Show the answer and explanationHide the explanation

   Answer: -4x - 9-4x - 9

   Distribute both: 2x - 6 - 6x - 3. Note the -3 multiplies both terms in the second bracket, giving -3 rather than +3. Collecting gives -4x - 9.Distribute both: 2x - 6 - 6x - 3. Note the -3 multiplies both terms in the second bracket, giving -3 rather than +3. Collecting gives -4x - 9.

   How did you do?Got itMissed it
8. 8Equivalent expressionsStandard

   Which expression is equivalent to (6x² + 9x) / 3x, for x not equal to 0?Which expression is equivalent to (6x^2 + 9x) / 3x, for x not equal to 0?

   • A6x + 36x + 3
   • B2x² + 32x^2 + 3
   • C2x + 92x + 9
   • D2x + 32x + 3
   Show the answer and explanationHide the explanation

   Answer: 2x + 32x + 3

   Divide each term by 3x: 6x² / 3x = 2x and 9x / 3x = 3. Dividing only the first term is the common slip.Divide each term by 3x: 6x^2 / 3x = 2x and 9x / 3x = 3. Dividing only the first term is the common slip.

   How did you do?Got itMissed it
9. 9Equivalent expressionsStandard

   If 5(2x - 3) - 4(x - 2) = ax + b for every value of x, enter the value of a.If 5(2x - 3) - 4(x - 2) = ax + b for every value of x, enter the value of a.

   Student-produced response: write your own answer rather than choosing one.

   Show the answer and explanationHide the explanation

   Answer: 66

   Expanding gives 10x - 15 - 4x + 8 = 6x - 7, so a = 6 and b = -7. The commonest slip is distributing the -4 to only the first term inside its bracket, which leaves a = 6 but the wrong constant.Expanding gives 10x - 15 - 4x + 8 = 6x - 7, so a = 6 and b = -7. The commonest slip is distributing the -4 to only the first term inside its bracket, which leaves a = 6 but the wrong constant.

   How did you do?Got itMissed it
10. 10Equivalent expressionsStandard

    Which expression is equivalent to (x + 5)(x - 5) + 25?Which expression is equivalent to (x + 5)(x - 5) + 25?

    • Ax² + 25x^2 + 25
    • Bx² - 50x^2 - 50
    • Cx² + 10xx^2 + 10x
    • Dx²x^2
    Show the answer and explanationHide the explanation

    Answer: x²x^2

    The product is a difference of squares, x² - 25, and adding 25 cancels the constant exactly, leaving x². Expanding the bracket as if it were (x + 5)² produces the choice with a 10x term.The product is a difference of squares, x^2 - 25, and adding 25 cancels the constant exactly, leaving x^2. Expanding the bracket as if it were (x + 5)^2 produces the choice with a 10x term.

    How did you do?Got itMissed it
11. 11Equivalent expressionsStandard

    Which expression is equivalent to (3x - 2)²?Which expression is equivalent to (3x - 2)^2?

    • A9x² + 49x^2 + 4
    • B9x² - 12x + 49x^2 - 12x + 4
    • C9x² - 6x + 49x^2 - 6x + 4
    • D3x² - 12x + 43x^2 - 12x + 4
    Show the answer and explanationHide the explanation

    Answer: 9x² - 12x + 49x^2 - 12x + 4

    A squared binomial gives three terms: (3x)² = 9x², twice the product 2(3x)(-2) = -12x, and (-2)² = 4. Squaring each term separately drops the middle one entirely.A squared binomial gives three terms: (3x)^2 = 9x^2, twice the product 2(3x)(-2) = -12x, and (-2)^2 = 4. Squaring each term separately drops the middle one entirely.

    How did you do?Got itMissed it
12. 12Equivalent expressionsStandard

    If 4(2x + 3) - 5x = ax + b for every value of x, enter the value of b.If 4(2x + 3) - 5x = ax + b for every value of x, enter the value of b.

    Student-produced response: write your own answer rather than choosing one.

    Show the answer and explanationHide the explanation

    Answer: 1212

    Expanding gives 8x + 12 - 5x = 3x + 12, so a = 3 and b = 12. The constant comes only from the 4 times 3; the -5x contributes nothing to it.Expanding gives 8x + 12 - 5x = 3x + 12, so a = 3 and b = 12. The constant comes only from the 4 times 3; the -5x contributes nothing to it.

    How did you do?Got itMissed it
13. 13Equivalent expressionsStandard

    If 3(2x - 1) - 2(x - 4) = ax + b for every value of x, enter the value of a.If 3(2x - 1) - 2(x - 4) = ax + b for every value of x, enter the value of a.

    Student-produced response: write your own answer rather than choosing one.

    Show the answer and explanationHide the explanation

    Answer: 44

    Expanding gives 6x - 3 - 2x + 8 = 4x + 5, so a = 4 and b = 5. The sign on the second bracket matters twice: -2 times -4 adds 8.Expanding gives 6x - 3 - 2x + 8 = 4x + 5, so a = 4 and b = 5. The sign on the second bracket matters twice: -2 times -4 adds 8.

    How did you do?Got itMissed it
14. 14Equivalent expressionsChallenge

    If a = 3b and b = 2c, which expression gives a in terms of c?If a = 3b and b = 2c, which expression gives a in terms of c?

    • A6c6c
    • Bc/6c/6
    • C1.5c1.5c
    • D5c5c
    Show the answer and explanationHide the explanation

    Answer: 6c6c

    Substitute b = 2c into a = 3b: a = 3(2c) = 6c. Adding the coefficients rather than multiplying gives 5c, which is the trap.Substitute b = 2c into a = 3b: a = 3(2c) = 6c. Adding the coefficients rather than multiplying gives 5c, which is the trap.

    How did you do?Got itMissed it
15. 15Equivalent expressionsChallenge

    Which expression is equivalent to (3x + 2)(x - 5) - 3x²?Which expression is equivalent to (3x + 2)(x - 5) - 3x^2?

    • A13x - 1013x - 10
    • B-13x + 10-13x + 10
    • C6x² - 13x - 106x^2 - 13x - 10
    • D-13x - 10-13x - 10
    Show the answer and explanationHide the explanation

    Answer: -13x - 10-13x - 10

    Expanding the product gives 3x² - 15x + 2x - 10 = 3x² - 13x - 10. Subtracting 3x² cancels the squared term and leaves -13x - 10. Forgetting to subtract leaves the quadratic term in place; dropping a sign flips the linear term.Expanding the product gives 3x^2 - 15x + 2x - 10 = 3x^2 - 13x - 10. Subtracting 3x^2 cancels the squared term and leaves -13x - 10. Forgetting to subtract leaves the quadratic term in place; dropping a sign flips the linear term.

    How did you do?Got itMissed it