Rewriting Polynomials using Distributive Property

What math operation would you use to simplify the problem 2(x + 6)?

• Add

• Subtract

• Multiply

• Divide

Answer explanation

To simplify 2(x + 6), you would use multiplication. Distributing 2 to both terms inside the parentheses involves multiplying 2 by x and 2 by 6, making 'Multiply' the correct operation.

Choose the two terms that are alike.

• 6x

• 27

• -x

Answer explanation

The terms 6x and -x are alike because they both contain the variable 'x'. The other options, 27 and 4x^2, are not like these terms as they do not share the same variable component.

Which answer shows two like terms?

Answer explanation

The correct choice is 3x² and -7x², as both terms have the same variable part (x²) and can be combined. The other options contain terms that are not like terms, either differing in variable or degree.

Which of the following pairs are like terms?

Answer explanation

Like terms have the same variable part. Here, 2y and 3y both contain the variable y, making them like terms. The other pairs differ in their variables or exponents.

What operation is needed to combine the terms 5x and 3x?

• Addition

• Subtraction

• Multiplication

• Division

Answer explanation

To combine the terms 5x and 3x, you need to perform addition. This is because both terms are like terms, meaning they have the same variable part (x), allowing you to add their coefficients (5 + 3).

Like terms have the same ________ and ________.

• variable

• exponent

• coefficient

• constant

Answer explanation

Like terms must have the same variable and exponent. This means they share the same base and power, allowing them to be combined in algebraic expressions.

Which expression is equivalent to 24gh - 12g² + 18g?

• 6g (4h - 12g + 18)

• 12g (2h - 12g +18)

• 6g (4h - 2g + 3)

• 12g (2h - g + 3)

Answer explanation

To factor 24gh - 12g^2 + 18g, we can factor out 6g, resulting in 6g(4h - 2g + 3). This matches the correct choice, confirming that 6g(4h - 2g + 3) is equivalent to the original expression.

Answer explanation

To factor the expression 35m^2 - 63, we can factor out the greatest common factor, which is 7. This gives us 7(5m^2 - 9), making the correct choice 7(5m^2 - 9).

Answer explanation

To factor the expression 210d^2 - 63d, we first find the greatest common factor, which is 21d. Factoring this out gives us 21d(10d - 3), making the correct choice 21d(10d - 3).

Answer explanation

To factor -28x^2 + 35x, first factor out -7x, giving -7x(4x - 5). This matches the correct choice, which is -7x(4x - 5). The other options do not simplify to the original expression.