Simplify the algebraic expression 2(x + 5) – 3(x + 4).

A. x – 2
Incorrect. After distributing the 2 and -3, the x –values are 2x and -3x which equals –x.

B. -x + 4
Incorrect. After distributing the 2 and -3, combine like terms. The constants were added incorrectly.

C. x + 14
Incorrect. After distributing the 2 and -3 (make sure the negative is distributed throughout the paraenthesis), combine like terms.

D. -x – 2
Correct!

Which expression is equivalent to 3 4 (4x – 16y) + (7y – 13x)?

A. -10x – 25y
Incorrect. After distributing 3 4 , combine like terms. The y terms are added incorrectly.

B. 10x – 29y
Incorrect. After distributing 3 4 , combine like terms. The y terms are added incorrectly.

C. -10x –5y
Correct!

D. -10x – 29y
Incorrect. After distributing 3 4 , combine like terms. The y terms are added incorrectly.

Simplify the polynomial.

-2x(6x – 3) + 8x – (14 – 16x²).

A. 4x² + 2x – 14
Incorrect. After distributing the -2x and -1, combine like terms. The x – terms were added incorrectly.

B. 4x² + 14x – 14
Correct!

C. -28x² + 14x – 14
Incorrect. After distributing the -2x and -1, combine like terms. The x^2 terms were added incorrectly.

Simplify the algebraic expression.

5(x² – 2xy) + 2(3x² – 12xy + 12).

A. 11x² – 34xy + 24
Correct!

B. 11x² – 14xy + 24
Incorrect. After distributing the 5 and 2, combine like terms. The xy – term was added incorrectly.

C. 11x² – 14xy + 12
Incorrect. After distributing the 5 and the 2, combine like terms. The xy-terms and constants were added incorrectly.

D. 11x² + 14xy – 24
Incorrect. After distributing the 5 and 2, combine like terms. The xy- term and constant were added incorrectly.

You are selling T-shirts. The cost of buying and designing the shirts are 3(x + 1)(x − 4) where x represents the number of T-shirts. Your income will be determined by the expression 2(4x² – 6x – 9). The profit you make is determined by your cost (negative) and how many you sell (positive). Simplify the algebraic expression -3(x + 1)(x − 4) + 2(4x² − 6x − 9) that represents the amount of profit in dollars that you'll make selling making and selling x T-shirts.

A. 5x² – 12x – 6
Incorrect. The x^2 terms were added correctly. The x – terms were added incorrectly.

B. 5x² – 3x – 6
Correct!

C. 8x² – 18x – 9
Incorrect. First multiply the two binomials then distribute the -3 and 2. The x^2 terms are -3x^2 and 8x^2, equaling 5x^2. Continue to add the like terms.

D. 11x² – 12x – 6
Incorrect. First multiply the two binomials then distribute the -3 and 2. The x^2 terms are -3x^2 and 8x^2, equaling 5x^2. Continue to add the like terms.