Expanding Brackets Practice Question

Expanding brackets (also known as "expanding parentheses") is a method in algebra where we remove brackets by multiplying each term inside the bracket by the term outside it.

Expanding brackets is commonly used when dealing with expressions like a(b + c) or more complex ones like (x + 2)(x + 3).

Examples of Expanding Brackets

Example 1: Expand: 4(x + 7)

Solution:

Given expression: 4(x + 7)

Multiply term outside the bracket by each term inside the bracket:

4(x + 7) = 4 × x + 4 × 7

Simplify: = 4x + 28

4(x + 7) = 4x + 28

Example 2: Expand: (x + 5)(x - 2) Using FOIL

Solution:

Apply FOIL method (First, Outer, Inner, Last):

First: x × x = x²
Outer: x × -2 = -2x
Inner: 5 × x = 5x
Last: 5 × -2 = -10

Combine terms: x² - 2x + 5x - 10

Simplify by combining like terms: = x² + 3x - 10

Example 3: Expand 3(x + 2)(x − 5)

Solution:

• First: x⋅x = x²
• Outside: x⋅(−5) = −5x
• Inside: 2⋅x = 2x
• Last: 2⋅(−5) = −10

Combine terms: x² − 5x + 2x − 10 = x² − 3x − 10

Now multiply each term by 3: 3(x² − 3x − 10) = 3x² − 9x − 30

Result: 3x² − 9x − 30

Example 4: Expand: (x + 4)²

Solution:

Given expression: (x + 4)²

Applying formula: (a + b)² = a² + 2ab + b²

(x + 4)² = x² + 2 × (x × 4) + 4²

Calculate each term: = x² + 8x + 16

Example 5: Expand (x + 1)(x - 2)(x + 3)

Solution:

Expand the first two brackets: (x + 1)(x - 2) = x² - 2x + x - 2 = x² - x - 2
Multiply the result by (x + 3): (x² - x - 2)(x + 3) = x² · x + x² · 3 - x · x - x · 3 - 2 · x - 2 · 3
Calculate each term: = x³ + 3x² - x² - 3x - 2x - 6
Simplify: = x³ + 2x² - 5x - 6

Result: x³ + 2x² - 5x - 6

Example 6: (2x - 3y)(x + 4y)

Solution:

Use foild method,

• First: 2x · x = 2x²
• Outside: 2x · 4y = 8xy
• Inside: -3y · x = -3xy
• Last: -3y · 4y = -12y²

Combine like terms: 2x² + 8xy - 3xy - 12y² = 2x² + 5xy - 12y²

Result: 2x² + 5xy - 12y²

Practice Questions on Expanding Brackets

Question 1. Expand: 5(x + 2)

Question 2. Expand: -3(2x - 4)

Question 3. Expand: (x + 6)(x - 3)

Question 4. Expand: (2x + 5)(x - 1)

Question 5. Expand and Simplify: (x - 4)²

Question 6. Expand: (3x + 2)(x - 5)

Question 7. Expand and Simplify: (x + 3)(x - 2)(x + 1)

Answer Key

1. 5(x + 2) = 5x + 10
2. -3(2x - 4) = -6x + 12
3. (x + 6)(x - 3) = x² + 3x - 18
4. (2x + 5)(x - 1) = 2x² + 3x - 5
5. (x - 4)² = x² - 8x + 16
6. (3x + 2)(x - 5) = 3x² - 15x +2x - 10 = 3x² - 13x - 10
7. (x + 3)(x - 2)(x + 1) = x³ + 2x² - 5x - 6

Read More,

• BODMAS Rule
• PEMDAS Rule 
• Order Of Operations