Simplifying Algebraic Expressions

Which of the following is equivalent to...

y + y + y + y

• 4y

• y4

• y⁴

• 4 + y

Answer explanation

The expression y + y + y + y represents adding y four times. This can be simplified to 4y, which is the correct choice. The other options do not represent this sum correctly.

Which of the following is equivalent?

• 4y

• y4

• y⁴

• 4 + y

Answer explanation

The expression y^4 represents y raised to the power of 4, which is equivalent to the correct answer. The other options either represent multiplication or addition, which are not equivalent to y^4.

Which of the following is equivalent to...?

• 8y

• y15

• y¹⁵

• y⁸

Answer explanation

The expression equivalent to the given question is y raised to the power of 8, which is represented as y^8. This matches the correct answer choice, making it the right option.

Which of the following is equivalent to this expression?

• 
• 
• 
• 

Simplify the expression.

(Do NOT use spaces.)

Answer explanation

The expression simplifies to 0 because the terms cancel each other out. Thus, the correct answer is 0.

This expression when simplified is equal to ​​ (a)   .

• 12mn

• 8mn

• 9mn

• 2m * 6n

• 12nm

Answer explanation

To simplify the expression, combine like terms. The expression simplifies to 12mn, which matches the correct answer choice. Other options do not equal the simplified form.

Match the following:

• 6m + 4n

• 
• 2m + 6n

• 
• 2m² + 2m - n

• 
• 12mn

• 
• 7m - 11

• 

Simplify 3ab * 3.

• 9a * b

• 3a + 3b

• 9a + 9b

• 9ab

Answer explanation

To simplify 3ab * 3, multiply the coefficients: 3 * 3 = 9. Thus, the expression becomes 9ab. The correct answer is 9ab.

Match the following:

• 16ab²c

• 4ab * 4abc

• 16a³b²c³

• 4abc * 4b

• 108a¹³

• 4abc * 4a²bc²

• 3

• (2a²)² * (3a³)³

• 16a²b²c

• (2a + a)/a

Simplify:
3a(5a² + 8a + 2)

• 15a³ + 24a² + 6a

• 10a³ + 24a + 6

• 8a³ + 11a² + 6a

• 15a³ + 24a + 6

Answer explanation

To simplify, distribute 3a across the terms in the parentheses: 3a * 5a^2 = 15a^3, 3a * 8a = 24a^2, and 3a * 2 = 6a. Combining these gives 15a^3 + 24a^2 + 6a, which matches the correct answer.