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Exam technique: “show that” questions practice questions with answers

Foundation and Higher · Grade 5

A second set of exam technique: “show that” questions questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

Expand and simplify 4(x+2)-x.

Show answer

Answer: 3x+8

  1. Expand: 4x + 8 - x.
  2. Collect like terms: 3x + 8.
  • Method (1): Expand: 4x + 8 - x.
  • Accuracy (1): Collect like terms: 3x + 8.

Question 2 Easy

Expand and simplify 5(x+1)-x.

Show answer

Answer: 4x+5

  1. Expand: 5x + 5 - x.
  2. Collect like terms: 4x + 5.
  • Method (1): Expand: 5x + 5 - x.
  • Accuracy (1): Collect like terms: 4x + 5.

Question 3 Medium

Expand and simplify (x+3)(x+5)-x^2.

Show answer

Answer: 8x+15

  1. Expand: x^2 + 8x + 15 - x^2.
  2. Cancel x^2: 8x + 15.
  • Method (1): Expand: x^2 + 8x + 15 - x^2.
  • Accuracy (1): Cancel x^2: 8x + 15.

Question 4 Medium

Expand and simplify (x+2)(x+6)-x^2.

Show answer

Answer: 8x+12

  1. Expand: x^2 + 8x + 12 - x^2.
  2. Cancel x^2: 8x + 12.
  • Method (1): Expand: x^2 + 8x + 12 - x^2.
  • Accuracy (1): Cancel x^2: 8x + 12.

Question 5 Hard

Expand (x+6)(x+2).

Show answer

Answer: x^2+8x+12

  1. Multiply terms: x^2 + 2x + 6x + 12.
  2. Simplify terms: x^2 + 8x + 12.
  • Method (1): Multiply terms: x^2 + 2x + 6x + 12.
  • Accuracy (1): Simplify terms: x^2 + 8x + 12.

Question 6 Hard

Expand (x+5)(x+2).

Show answer

Answer: x^2+7x+10

  1. Multiply terms: x^2 + 2x + 5x + 10.
  2. Combine like terms: x^2 + 7x + 10.
  • Method (1): Multiply terms: x^2 + 2x + 5x + 10.
  • Accuracy (1): Combine like terms: x^2 + 7x + 10.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

Expand and simplify 6(x+3)-x.

Show answer

Answer: 5x+18

  1. Expand bracket: 6x + 18 - x.
  2. Collect like terms: 5x + 18.
  • Method (1): Expand bracket: 6x + 18 - x
  • Accuracy (1): Combine x terms: 5x+18

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

How do you expand a single bracket like 3(x + 4)?

  1. Multiply both terms inside by 3: 3x + 12
  2. Multiply only x: 3x + 4
  3. Add 3: x + 7
Show answer

Multiply both terms inside by 3: 3x + 12 Distributive law multiplies every term inside by the factor outside.

Check 2

What is 3(x + 4) - x simplified?

  1. 2x + 12
  2. 3x + 12
  3. 3x + 4
Show answer

2x + 12 3x + 12 - x = 2x + 12.

Check 3

What is 2(x + 5) - x simplified?

  1. x + 10
  2. 2x + 10
  3. 2x + 5
Show answer

x + 10 2x + 10 - x = x + 10.

Check 4

What is (x + 2)(x + 3) expanded?

  1. x^2 + 5x + 6
  2. x^2 + 6
  3. 5x + 6
Show answer

x^2 + 5x + 6 x^2 + 3x + 2x + 6 = x^2 + 5x + 6.

Check 5

What is (x + 2)(x + 3) - x^2 simplified?

  1. 5x + 6
  2. x^2 + 5x + 6
  3. 6x + 5
Show answer

5x + 6 x^2 + 5x + 6 - x^2 = 5x + 6.

Check 6

What is (x + 1)(x + 4) - x^2 simplified?

  1. 5x + 4
  2. x^2 + 5x + 4
  3. 4x + 4
Show answer

5x + 4 x^2 + 5x + 4 - x^2 = 5x + 4.

Check 7

What is (x + 1)^2 expanded?

  1. x^2 + 2x + 1
  2. x^2 + 1
  3. 2x + 1
Show answer

x^2 + 2x + 1 (x + 1)(x + 1) = x^2 + 2x + 1.

Check 8

What is (x + 1)^2 - x^2 simplified?

  1. 2x + 1
  2. x^2 + 2x + 1
  3. 1
Show answer

2x + 1 x^2 + 2x + 1 - x^2 = 2x + 1.

Check 9

What is (x + 3)^2 - x^2 simplified?

  1. 6x + 9
  2. 9x + 6
  3. x^2 + 6x + 9
Show answer

6x + 9 x^2 + 6x + 9 - x^2 = 6x + 9.

Check 10

What is (x + 4)(x + 1) expanded?

  1. x^2 + 5x + 4
  2. 5x + 4
  3. x^2 + 4
Show answer

x^2 + 5x + 4 x^2 + x + 4x + 4 = x^2 + 5x + 4.

Check 11

What is (x + 5)(x + 2) expanded?

  1. x^2 + 7x + 10
  2. 7x + 10
  3. x^2 + 10
Show answer

x^2 + 7x + 10 x^2 + 2x + 5x + 10 = x^2 + 7x + 10.

Check 12

Why does (x + a)^2 not equal x^2 + a^2?

  1. It produces a cross-term 2ax when expanded
  2. Because a is squared
  3. Only for negative numbers
Show answer

It produces a cross-term 2ax when expanded (x + a)(x + a) = x^2 + ax + ax + a^2 = x^2 + 2ax + a^2.

Check 13

What is 4(x + 2) - x simplified?

  1. 3x + 8
  2. 4x + 8
  3. 4x + 2
Show answer

3x + 8 4x + 8 - x = 3x + 8.

Check 14

What is 5(x + 1) - x simplified?

  1. 4x + 5
  2. 5x + 5
  3. 5x + 1
Show answer

4x + 5 5x + 5 - x = 4x + 5.

Check 15

What is (x + 3)(x + 5) - x^2 simplified?

  1. 8x + 15
  2. x^2 + 8x + 15
  3. 15x + 8
Show answer

8x + 15 x^2 + 8x + 15 - x^2 = 8x + 15.

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