Exploring the Distributive Property in Algebra

What does the distributive property allow us to do with algebraic expressions?

• Eliminate all variables from an expression

• Combine like terms inside parentheses

• Distribute a multiplier over terms within parentheses

• Solve for variables within parentheses

In the expression 2(3x + 4), what is the first step using the distributive property?

• Add 3x and 4

• Multiply 2 by 3x and 4 separately

• Divide 2 by 3x and 4

• Subtract 4 from 3x

How does the distributive property work with subtraction inside parentheses?

• It includes the subtraction sign as a negative with the term

• It cannot distribute over subtraction

• It only distributes positive numbers

• It changes subtraction to addition

What is the result of applying the distributive property to 7(a - 9)?

• 7a - 9

• 7a - 63

• 7a + 63

• 49a - 9

When combining like terms, what must be true about the terms?

• They must be on opposite sides of the equation

• They must have the same coefficient

• They must have the same variable and exponent

• They must both be constants

How can you simplify the expression 4 + 2(n + 6) using the distributive property?

• 6n + 24

• 2n + 10

• 6n + 10

• 2n + 16

What does combining like terms involve?

• Multiplying coefficients

• Canceling out negative signs

• Dividing exponents

• Adding or subtracting terms with the same variable

In the expression 5(x^2 - 3) + 10 - 4x, what is simplified first?

• Add 10 to -3

• Distribute 5 to x^2 and -3

• Combine x^2 and -4x

• Subtract 4x from 10

After distributing and combining like terms, what is the simplified form of 7g + 4(2g - 6h)?

• 15g - 3h

• 28g - 24h

• 11g - 24h

• 8g + 24h

What is the correct order of operations when applying the distributive property?

• Distribute, simplify, combine like terms

• Simplify, distribute, combine like terms

• Distribute, combine like terms, simplify

• Combine like terms, distribute, simplify