MATH SOLVE

3 months ago

Q:
# Simplify the expression. 3y3 – 2y[4y – y(y – 3)] – [2y(y + 1) – 3y(y2 –1)]

Accepted Solution

A:

The first step for solving this expression is to distribute -y through the parenthesis.

3y³ - 2y × (4y - y² + 3y) - (2y × (y + 1) - 3y × (y² - 1))

Distribute 2y through the parenthesis.

3y³ - 2y × (4y - y² + 3y) - (2y² + 2y - 3y × (y² - 1))

Now distribute -3y through the parenthesis.

3y³ - 2y × (4y - y² + 3y) - (2y² + 2y - 3y³ + 3y)

Collect the like terms in the first set of the parenthesis.

3y³ - 2y × (7y - y²) - (2y² + 2y - 3y³ + 3y)

Collect the like terms in the second set of the parenthesis.

3y³ - 2y × (7y - y²) - (2y² + 5y - 3y³)

Distribute -2y through the parenthesis.

3y³ - 14y² + 2y³ - (2y² + 5y - 3y³)

Remember that when there is a "-" sign in front of the parenthesis,, you must change the sign of each term in the parenthesis. This will change the expression to the following:

3y³ - 14y² + 2y³ - 2y² - 5y + 3y³

Collect the like terms with an exponent of 3.

8y³ - 14y² - 2y² - 5y

Lastly,, collect like terms that have an exponent of 2.

8y³ - 16y² - 5y

Since we cannot simplify the expression any further,, the correct answer is going to be 8y³ - 16y² - 5y.

Let me know if you have any further questions.

:)

3y³ - 2y × (4y - y² + 3y) - (2y × (y + 1) - 3y × (y² - 1))

Distribute 2y through the parenthesis.

3y³ - 2y × (4y - y² + 3y) - (2y² + 2y - 3y × (y² - 1))

Now distribute -3y through the parenthesis.

3y³ - 2y × (4y - y² + 3y) - (2y² + 2y - 3y³ + 3y)

Collect the like terms in the first set of the parenthesis.

3y³ - 2y × (7y - y²) - (2y² + 2y - 3y³ + 3y)

Collect the like terms in the second set of the parenthesis.

3y³ - 2y × (7y - y²) - (2y² + 5y - 3y³)

Distribute -2y through the parenthesis.

3y³ - 14y² + 2y³ - (2y² + 5y - 3y³)

Remember that when there is a "-" sign in front of the parenthesis,, you must change the sign of each term in the parenthesis. This will change the expression to the following:

3y³ - 14y² + 2y³ - 2y² - 5y + 3y³

Collect the like terms with an exponent of 3.

8y³ - 14y² - 2y² - 5y

Lastly,, collect like terms that have an exponent of 2.

8y³ - 16y² - 5y

Since we cannot simplify the expression any further,, the correct answer is going to be 8y³ - 16y² - 5y.

Let me know if you have any further questions.

:)