OAR OAR Math Skills: Algebraic Expressions Questions and Answers 3

Question 1

Expand and simplify: (2x + 3)(x - 7)

Accepted Answer

2x² - 11x - 21

Answer

Using FOIL: 2x·x + 2x·(-7) + 3·x + 3·(-7) = 2x² - 14x + 3x - 21 = 2x² - 11x - 21.

Question 2

Simplify the rational expression: (x² - 16)/(x + 4)

Accepted Answer

x - 4

Answer

Factor the numerator as a difference of squares (x+4)(x-4) and cancel the common factor (x+4).

Question 3

If 3(x - 2) = 2(x + 5), what is the value of x?

Accepted Answer

16

Answer

Distribute to get 3x - 6 = 2x + 10, then subtract 2x and add 6 to both sides giving x = 16.

Question 4

Which expression represents the product of (a - b)² ?

Accepted Answer

a² - 2ab + b²

Answer

The square of a binomial (a-b)² expands to a² - 2ab + b² using the perfect square trinomial pattern.

Question 5

Combine like terms: 7m²n - 3mn² + 2m²n + 5mn²

Accepted Answer

9m²n + 2mn²

Answer

Combine m²n terms (7+2=9) and mn² terms (-3+5=2) to get 9m²n + 2mn².

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