Expanding Double Brackets

1 / 6

Q: Simplify $(x + 3) (x + 2)$ .

x^{2} + 5 x + 3

x^{2} + 6 x + 6

x^{2} + 5 x + 6

x^{2} + 3 x + 2

Feedback: Not quite! First, multiply $x$ by $x$ to get $x^{2}$ , then multiply $x$ by $2$ to get $2 x$ . Next, multiply $3$ by $x$ to get $3 x$ , and $3$ by $2$ to get $6$ . Finally, add all the terms together: $x^{2} + 2 x + 3 x + 6$ . Combining $2 x$ and $3 x$ gives $5 x$ , so the final answer is $x^{2} + 5 x + 6$ .

Feedback: Well done! First, multiply $x$ by $x$ to get $x^{2}$ , then multiply $x$ by $2$ to get $2 x$ . Next, multiply $3$ by $x$ to get $3 x$ , and $3$ by $2$ to get $6$ . Finally, add all the terms together: $x^{2} + 2 x + 3 x + 6$ . Combining $2 x$ and $3 x$ gives $5 x$ , so the final answer is $x^{2} + 5 x + 6$ .

2 / 6

Q: Simplify $(x + 4) (x + 1)$ .

x^{2} + 4 x + 5

x^{2} + 5 x + 5

x^{2} + 4 x + 4

x^{2} + 5 x + 4

Feedback: Not quite! First, multiply $x$ by $x$ to get $x^{2}$ , then multiply $x$ by $1$ to get $x$ . Next, multiply $4$ by $x$ to get $4 x$ , and $4$ by $1$ to get $4$ . Finally, combine all terms: $x^{2} + x + 4 x + 4$ . Adding $x$ and $4 x$ gives $5 x$ , so the final answer is $x^{2} + 5 x + 4$ .

Feedback: Well done! First, multiply $x$ by $x$ to get $x^{2}$ , then multiply $x$ by $1$ to get $x$ . Next, multiply $4$ by $x$ to get $4 x$ , and $4$ by $1$ to get $4$ . Finally, combine all terms: $x^{2} + x + 4 x + 4$ . Adding $x$ and $4 x$ gives $5 x$ , so the final answer is $x^{2} + 5 x + 4$ .

3 / 6

Q: Simplify $(2 x + 1) (x + 4)$ .

2 x^{2} + 6 x + 4

2 x^{2} + 9 x + 4

2 x^{2} + 7 x + 4

2 x^{2} + 5 x + 4

Feedback: Not quite! First, multiply $2 x$ by $x$ to get $2 x^{2}$ , then multiply $2 x$ by $4$ to get $8 x$ . Next, multiply $1$ by $x$ to get $x$ , and $1$ by $4$ to get $4$ . Combine all terms: $2 x^{2} + 8 x + x + 4$ . Adding $8 x$ and $x$ gives $9 x$ , so the final answer is $2 x^{2} + 9 x + 4$ .

Feedback: Well done! First, multiply $2 x$ by $x$ to get $2 x^{2}$ , then multiply $2 x$ by $4$ to get $8 x$ . Next, multiply $1$ by $x$ to get $x$ , and $1$ by $4$ to get $4$ . Combine all terms: $2 x^{2} + 8 x + x + 4$ . Adding $8 x$ and $x$ gives $9 x$ , so the final answer is $2 x^{2} + 9 x + 4$ .

4 / 6

Q: Simplify $(x - 2) (2 x - 3)$ .

2 x^{2} - 5 x - 6

2 x^{2} - 5 x + 6

2 x^{2} - 7 x + 6

2 x^{2} - 4 x + 6

Feedback: Not quite! First, multiply $x$ by $2 x$ to get $2 x^{2}$ , then multiply $x$ by $- 3$ to get $- 3 x$ . Next, multiply $- 2$ by $2 x$ to get $- 4 x$ , and $- 2$ by $- 3$ to get $6$ . Finally, combine all terms: $2 x^{2} - 3 x - 4 x + 6$ . Adding $- 3 x$ and $- 4 x$ gives $- 7 x$ , so the final answer is $2 x^{2} - 7 x + 6$ .

Feedback: Well done! First, multiply $x$ by $2 x$ to get $2 x^{2}$ , then multiply $x$ by $- 3$ to get $- 3 x$ . Next, multiply $- 2$ by $2 x$ to get $- 4 x$ , and $- 2$ by $- 3$ to get $6$ . Finally, combine all terms: $2 x^{2} - 3 x - 4 x + 6$ . Adding $- 3 x$ and $- 4 x$ gives $- 7 x$ , so the final answer is $2 x^{2} - 7 x + 6$ .

5 / 6

Q: Simplify $(3 x - 2) (x + 4)$ .

3 x^{2} + 12 x - 8

3 x^{2} + 10 x + 8

3 x^{2} + 8 x - 8

3 x^{2} + 10 x - 8

Feedback: Not quite! First, multiply $3 x$ by $x$ to get $3 x^{2}$ , then multiply $3 x$ by $4$ to get $12 x$ . Next, multiply $- 2$ by $x$ to get $- 2 x$ , and $- 2$ by $4$ to get $- 8$ . Finally, combine all terms: $3 x^{2} + 12 x - 2 x - 8$ . Adding $12 x$ and $- 2 x$ gives $10 x$ , so the final answer is $3 x^{2} + 10 x - 8$ .

Feedback: Well done! First, multiply $3 x$ by $x$ to get $3 x^{2}$ , then multiply $3 x$ by $4$ to get $12 x$ . Next, multiply $- 2$ by $x$ to get $- 2 x$ , and $- 2$ by $4$ to get $- 8$ . Finally, combine all terms: $3 x^{2} + 12 x - 2 x - 8$ . Adding $12 x$ and $- 2 x$ gives $10 x$ , so the final answer is $3 x^{2} + 10 x - 8$ .

6 / 6

Q: Simplify $(- 5 x + 3) (4 - 2 x)$ .

- 10 x^{2} - 26 x + 12

10 x^{2} + 26 x + 12

- 10 x^{2} + 26 x - 12

10 x^{2} - 26 x + 12

Feedback: Not quite! First, multiply $- 5 x$ by $4$ , which gives $- 20 x$ . Next, multiply $- 5 x$ by $- 2 x$ , resulting in $+ 10 x^{2}$ . Then, multiply $3$ by $4$ , which gives $12$ . Finally, multiply $3$ by $- 2 x$ , resulting in $- 6 x$ . Combining all the terms, we get $- 20 x + 10 x^{2} + 12 - 6 x$ . Simplifying the like terms $- 20 x$ and $- 6 x$ , we get $- 26 x$ . So, the final simplified expression is $10 x^{2} - 26 x + 12$ .

Feedback: Well done! First, multiply $- 5 x$ by $4$ , which gives $- 20 x$ . Next, multiply $- 5 x$ by $- 2 x$ , resulting in $+ 10 x^{2}$ . Then, multiply $3$ by $4$ , which gives $12$ . Finally, multiply $3$ by $- 2 x$ , resulting in $- 6 x$ . Combining all the terms, we get $- 20 x + 10 x^{2} + 12 - 6 x$ . Simplifying the like terms $- 20 x$ and $- 6 x$ , we get $- 26 x$ . So, the final simplified expression is $10 x^{2} - 26 x + 12$ .

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Expanding Double Brackets

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Expanding Double Brackets

🎬 Video Tutorial

Membership Required

📂 Revision Cards

🍪 Quiz Time - Practice Now!​

🎩 AI Math Solver (ChatCat)

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🍪 Quiz Time - Practice Now!