GCSE Simplifying and single brackets Practice Questions

Free GCSE Simplifying and single brackets practice questions with full step-by-step worked solutions. Covers collecting like terms, two variables, constants, multiplying terms. Practise exam-style problems and check your method.

collecting like termstwo variablesconstantsmultiplying termsindicesexpanding brackets
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
Simplify 3x+5x3x + 5x.
Show worked solution

Worked solution

  1. Identify the like terms

    3x+5x3x + 5x

    Both terms contain the letter x, so they are like terms.

  2. Add the coefficients

    3x+5x=(3+5)x3x + 5x = (3 + 5)x

    Add the numbers in front of x: 3+5=83 + 5 = 8.

  3. State the answer

    8x8x

    The simplified expression is 8x.

Answer
8x8x
Question 2
2 markseasy
Simplify 6c+2d−c+3d6c + 2d - c + 3d.
Show worked solution

Worked solution

  1. Group each letter

    (6c−1c)+(2d+3d)(6c - 1c) + (2d + 3d)

    c on its own is 1c; mind the minus sign.

  2. Combine each group

    5c+5d5c + 5d

    6c−c=5c6c - c = 5c and 2d+3d=5d2d + 3d = 5d.

  3. State the answer

    5c+5d5c + 5d

    The answer is 5c + 5d.

Answer
5c+5d5c + 5d
Question 3
2 marksintermediate
Simplify 7ab+2ab−3ab7ab + 2ab - 3ab.
Show worked solution

Worked solution

  1. Check the terms are alike

    7ab, 2ab, 3ab7ab,\ 2ab,\ 3ab

    Every term contains the same product ab, so they are like terms.

  2. Combine the coefficients

    (7+2−3)ab(7 + 2 - 3)ab

    Work along the line: 7 + 2 - 3.

  3. Work out the number

    7+2−3=67 + 2 - 3 = 6

    This gives 6 lots of ab.

  4. Check by substitution

    a=2, b=3:original=36,answer=36a = 2,\ b = 3:\quad \text{original} = 36,\quad \text{answer} = 36

    Substituting a=2a = 2, b=3b = 3 into the original expression and into the answer both give 36, so the simplification is correct.

  5. Note the general rule

    ax+bx=(a+b)xax + bx = (a + b)x

    Only like terms (same letter and power) can be combined; add their coefficients and keep the letter unchanged.

  6. State the answer

    6ab6ab

    The simplified expression is 6ab.

Answer
6ab6ab
Question 4
3 markshard
Factorise fully 7x2+14x7x^2 + 14x.
Show worked solution

Worked solution

  1. Find the number factor

    HCF of 7 and 14=7\text{HCF of } 7 \text{ and } 14 = 7

    7 divides both 7 and 14.

  2. Find the letter factor

    x2 and x share xx^2 \text{ and } x \text{ share } x

    Both terms contain x.

  3. State the common factor

    7x7x

    The full common factor is 7x.

  4. Divide each term by 7x

    7x2÷7x=x, 14x÷7x=27x^2 \div 7x = x,\ 14x \div 7x = 2

    Find the bracket contents.

  5. Check by substitution

    x=2:original=56,answer=56x = 2:\quad \text{original} = 56,\quad \text{answer} = 56

    Substituting x=2x = 2 into the original expression and into the answer both give 56, so the simplification is correct.

  6. Note the general rule

    ab+ac=a(b+c)ab + ac = a(b + c)

    To factorise, take out the highest common factor, then write what is left inside the bracket.

  7. Check by substitution

    x=3:original=105,answer=105x = 3:\quad \text{original} = 105,\quad \text{answer} = 105

    Substituting x=3x = 3 into the original expression and into the answer both give 105, so the simplification is correct.

  8. Avoid the common error

    6x2+9x≠3(2x2+3x)6x^2 + 9x \ne 3(2x^2 + 3x)

    Taking out only the number is not full factorisation — if the terms still share a letter, include it in the common factor.

  9. Check by substitution

    x=1:original=21,answer=21x = 1:\quad \text{original} = 21,\quad \text{answer} = 21

    Substituting x=1x = 1 into the original expression and into the answer both give 21, so the simplification is correct.

  10. State the answer

    7x(x+2)7x(x + 2)

    The fully factorised form is 7x(x + 2).

Answer
7x(x+2)7x(x + 2)
Question 5
6 markschallenging
Expand and simplify 3x(x+4)+2(x2−x)−5x3x(x + 4) + 2(x^2 - x) - 5x.
Show worked solution

Worked solution

  1. Expand the first bracket

    3x(x+4)=3x2+12x3x(x + 4) = 3x^2 + 12x

    Multiply x and 4 by 3x.

  2. Expand the second bracket

    2(x2−x)=2x2−2x2(x^2 - x) = 2x^2 - 2x

    Multiply x2x^2 and x by 2.

  3. Bring down the last term

    −5x- 5x

    The lone term is -5x.

  4. Group the x2x^2 terms

    3x2+2x2=5x23x^2 + 2x^2 = 5x^2

    3+2=53 + 2 = 5.

  5. Group the x terms

    12x−2x−5x=5x12x - 2x - 5x = 5x

    12−2−5=512 - 2 - 5 = 5.

  6. Write the result

    5x2+5x5x^2 + 5x

    Put the x2x^2 term first, then the x term.

  7. Check by substitution

    x=2:original=30,answer=30x = 2:\quad \text{original} = 30,\quad \text{answer} = 30

    Substituting x=2x = 2 into the original expression and into the answer both give 30, so the simplification is correct.

  8. Note the general rule

    a(b+c)=ab+aca(b + c) = ab + ac

    To expand a single bracket, multiply the term outside by every term inside.

  9. Check by substitution

    x=3:original=60,answer=60x = 3:\quad \text{original} = 60,\quad \text{answer} = 60

    Substituting x=3x = 3 into the original expression and into the answer both give 60, so the simplification is correct.

  10. Avoid the common error

    3(2x−5)≠6x−53(2x - 5) \ne 6x - 5

    A common mistake is to multiply only the first term. Every term inside the bracket must be multiplied.

  11. Check by substitution

    x=1:original=10,answer=10x = 1:\quad \text{original} = 10,\quad \text{answer} = 10

    Substituting x=1x = 1 into the original expression and into the answer both give 10, so the simplification is correct.

  12. Reflect

    ✓\checkmark

    The expression is now fully simplified and cannot be reduced any further.

  13. Check by substitution

    x=5:original=150,answer=150x = 5:\quad \text{original} = 150,\quad \text{answer} = 150

    Substituting x=5x = 5 into the original expression and into the answer both give 150, so the simplification is correct.

  14. Check by substitution

    x=10:original=550,answer=550x = 10:\quad \text{original} = 550,\quad \text{answer} = 550

    Substituting x=10x = 10 into the original expression and into the answer both give 550, so the simplification is correct.

  15. State the answer

    5x2+5x5x^2 + 5x

    The simplified expression is 5x2+5x5x^2 + 5x.

Answer
5x2+5x5x^2 + 5x

Unlock 65 more Simplifying and single brackets questions

Create a free account to work through every GCSE Simplifying and single brackets question with instant step-by-step worked solutions, progress tracking and interactive lessons.

  • Full worked solutions for every question
  • Interactive lessons and instant feedback
  • Track your mastery across every topic
Create a Free Account

No card required · Free forever

More Simplifying and single brackets practice

Hard QuestionsWorked Solutions

Related Algebra topics

Algebraic fractionsEquation of a circleCoordinatesCubic and reciprocal graphsExponential and trig graphsExpanding binomials