/
Expanding Algebraic Brackets
Save to my account
Sign up
Expanding Algebraic Brackets
Expanding Algebraic Brackets
Study
1
Question
How do you expand a single bracket like 5(x + 2)?
Answer
Multiply the term outside the bracket by each term inside the bracket.
2
Question
What is the result of expanding 5(x + 2)?
Answer
\(5x + 10\)
3
Question
How do you expand x(x + 9)?
Answer
Multiply x by each term inside the bracket: x times x and x times 9.
4
Question
What is the expanded form of x(x + 9)?
Answer
\(x^2 + 9x\)
5
Question
What does (x + 3)(x + 8) represent in terms of multiplication?
Answer
x plus 3 lots of (x + 8), so multiply x by both terms and 3 by both terms.
6
Question
What is the expansion of (x + 3)(x + 8) before simplifying?
Answer
\(x^2 + 8x + 3x + 24\)
7
Question
What is the simplified form of (x + 3)(x + 8)?
Answer
\(x^2 + 11x + 24\)
8
Question
In expanding (x + 5)(x - 3), what do you multiply by x?
Answer
Both terms in the second bracket: x*x and x*(-3), giving x² - 3x.
9
Question
What is the full expansion of (x + 5)(x - 3) before like terms?
Answer
\(x^2 - 3x + 5x - 15\)
10
Question
What is the simplified result of expanding (x + 5)(x - 3)?
Answer
\(x^2 + 2x - 15\)
11
Question
How does the sign change when multiplying 5 by -3 in (x + 5)(x - 3)?
Answer
Positive times negative gives negative, so 5 * -3 = -15.
12
Question
What is x(x - 7) when expanding (x - 4)(x - 7)?
Answer
\(x^2 - 7x\)
13
Question
What is the expansion of (x - 4)(x - 7) before simplifying?
Answer
\(x^2 - 7x - 4x + 28\)
14
Question
What is the simplified form of (x - 4)(x - 7)?
Answer
\(x^2 - 11x + 28\)
15
Question
In (x - 4)(x - 7), why is the constant term positive?
Answer
Because -4 times -7 is positive 28, as negative times negative yields positive.
16
Question
What is 2x times (3x + 5) in expanding (2x + 1)(3x + 5)?
Answer
\(6x^2 + 10x\)
17
Question
What does 1 times (3x + 5) give in (2x + 1)(3x + 5)?
Answer
\(3x + 5\)
18
Question
What is the full simplified expansion of (2x + 1)(3x + 5)?
Answer
\(6x^2 + 13x + 5\)
19
Question
How do you expand (x + 3)^2 according to the video?
Answer
Treat it as (x + 3)(x + 3) and multiply each term by each term.
20
Question
What is the expansion of (x + 3)(x + 3) before like terms?
Answer
\(x^2 + 3x + 3x + 9\)
21
Question
What is the simplified form of (x + 3)^2?
Answer
\(x^2 + 6x + 9\)
22
Question
Why do you collect like terms after expanding brackets?
Answer
To simplify the expression by adding coefficients of similar terms like x terms.
23
Question
What is the general method to expand two brackets like (a + b)(c + d)?
Answer
Multiply each term in the first bracket by each term in the second, then simplify.
24
Question
How does the sign of the product change in expansions with negative terms?
Answer
Positive times negative is negative; negative times negative is positive.
25
Question
In (2x + 1)(3x + 5), what makes the x² term 6x²?
Answer
2x multiplied by 3x gives 2*3 * x*x = 6x².
26
Question
Compare the linear coefficients in (x + 3)(x + 8) and (x + 5)(x - 3).
Answer
11x from 8x + 3x; 2x from -3x + 5x due to the negative sign.
27
Question
What happens to like terms such as -7x and -4x in (x - 4)(x - 7)?
Answer
They combine to -11x by adding the coefficients.
28
Question
Why is expanding (x + 3)^2 similar to other double brackets?
Answer
It uses the same method since squared means (x + 3) times itself.
29
Question
In single bracket expansion, how is x(x + 9) different from 5(x + 2)?
Answer
Variable outside produces x² term; number outside produces linear terms only.