Expanding Double Brackets
Expanding double brackets means multiplying every term in one bracket by each term in the other. This binomial product uses (a+b)(c+d) = ac+ad+bc+bd to give four terms. You then collect like terms.
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The Distributive Law
- The distributive law means multiplying a term by everything inside the brackets.
- For example, .
Binomial Products: Formula
- A binomial product means multiplying two brackets together.
- For , multiply every pair to get .
Expanding Two Brackets: Example
- Always include the signs when multiplying terms.
- For example, .
Expanding with Negatives
- Rewrite subtraction as adding a negative before expanding.
- For example, .
Practice Questions
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Simplify .
Correct! 🎉 +10 pointsNot quite right
First, multiply x by x to get , then multiply x by 2 to get . Next, multiply 3 by x to get , and 3 by 2 to get 6. Finally, add all the terms together: .
Simplify .
Correct! 🎉 +10 pointsNot quite right
First, multiply x by x to get , then multiply x by 1 to get x. Next, multiply 4 by x to get , and 4 by 1 to get 4. Combining like terms gives .
Simplify .
Correct! 🎉 +20 pointsNot quite right
First, multiply by x to get , then multiply by 4 to get . Next, multiply 1 by x to get x, and 1 by 4 to get 4. Combining all terms gives .
Simplify .
Correct! 🎉 +20 pointsNot quite right
First, multiply x by to get , then multiply x by −3 to get . Next, multiply −2 by to get , and −2 by −3 to get 6. Combining like terms gives .
Simplify .
Correct! 🎉 +20 pointsNot quite right
First, multiply by x to get , then multiply by 4 to get . Next, multiply −2 by x to get , and −2 by 4 to get −8. Combining like terms gives .
Simplify .
Correct! 🎉 +30 pointsNot quite right
First, multiply by 4 to get , then multiply by to get . Next, multiply 3 by 4 to get 12, and 3 by to get . Combining all terms gives .
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Expanding double brackets: distribute and collect like terms
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Expanding double brackets means multiplying two binomials together to remove the brackets. Each term in the first bracket multiplies each term in the second bracket. You then add the resulting products and collect any like terms, turning the product into a single expanded expression.
The formula is (a + b)(c + d) = ac + ad + bc + bd. Every term in the first bracket multiplies every term in the second bracket, which produces four separate products. You then add these four products together and collect any like terms to reach the simplified answer.
First multiply each term in the first bracket by each term in the second bracket, giving four products. Then simplify by collecting like terms. In the worked example, 6x² + 4x − 3x − 2 becomes 6x² + x − 2 once you collect the two x terms.
Keep the sign attached to each term as you multiply, treating −1 as +(−1). Multiply the terms with their signs, so a negative times a negative gives a positive and a negative times a positive gives a negative. Then collect like terms to finish.
The two terms inside one bracket are already added together, so they stay as they are. You only multiply across the two brackets, pairing each term in the first bracket with each term in the second. Multiplying terms from the same bracket would change the expression you were given.