expressions and collecting terms and expanding brackets Flashcards
What does it mean to expand brackets in algebra?
Expanding brackets means to multiply each term inside the brackets by the term outside the brackets.
True or False: (x + 2)(x + 3) expands to x^2 + 5x + 6.
True
What is the first step in expanding the expression 3(x + 4)?
Multiply 3 by both x and 4.
What is the result of expanding 2(a + 5b)?
2a + 10b
Fill in the blank: To collect like terms, you combine terms that have the same __________.
variables
What is the coefficient of x in the expression 5x + 3?
5
Expand the expression (2x)(3x + 4).
6x^2 + 8x
True or False: The expression 4x + 2x can be simplified to 6x.
True
What is the result of collecting like terms in the expression 7x - 3x + 5?
4x + 5
What is the expanded form of (x + 1)^2?
x^2 + 2x + 1
True or False: In the expression 5(x + 2) + 3(x + 4), the term 5x is a like term with 3x.
False
Expand the expression 4(x - 3).
4x - 12
What is the simplified form of 2x + 3x + 4?
5x + 4
Fill in the blank: The distributive property states that a(b + c) = __________.
ab + ac
What do you get when you expand (x - 2)(x + 5)?
x^2 + 3x - 10
True or False: Collecting like terms can only be done with numerical coefficients.
False
What is the result of expanding 3(x + 2y - 4)?
3x + 6y - 12
Provide the simplified form of 6y + 2y - 4y.
4y
What happens to the signs when you expand (x - 3)(x - 2)?
The signs remain the same for the terms inside the brackets.
What is the expanded form of (2x + 3)(x + 1)?
2x^2 + 5x + 3
True or False: You can collect the terms 2x^2 and 3x^2.
True
Expand the expression (3x + 2)(2x - 5).
6x^2 - 15x + 4x - 10
Fill in the blank: Like terms must have the same __________ and __________.
variables, exponents
What is the simplified form of 8x - 2x + 7?
6x + 7
Expand the expression 5(2x + 3) - 2(3x - 1).
10x + 15 - 6x + 2
True or False: The expression 2a + 3b - 2a can be simplified to 3b.
True
What is the result of expanding (x + 4)(x - 4)?
x^2 - 16
Fill in the blank: The expression 2(x + 3) + 4(x + 1) simplifies to __________.
6x + 10
What do you get when you collect like terms in the expression 9y - 3y + 2?
6y + 2
Expand the expression (x + 2)(x + 5).
x^2 + 7x + 10
True or False: In the expression 4x + 5 - 2x, you can combine 4x and -2x.
True
What is the coefficient of y in the expression 3y + 7?
3
What is the expanded form of (x + 1)(x - 1)?
x^2 - 1
Fill in the blank: To simplify the expression 7x - x, you would get __________.
6x
Expand the expression (2x - 3)(x + 4).
2x^2 + 5x - 12
What is the result of simplifying the expression 5x + 2x - 3x?
4x
True or False: To expand (a + b)(c + d), you apply the distributive property twice.
True
What do you get when you collect like terms in the expression 10a + 3b - 2a + 4b?
8a + 7b
Expand the expression (x + 3)^2.
x^2 + 6x + 9
Fill in the blank: The expression 4(x + 2) - 3(x + 1) simplifies to __________.
x + 5
