Question

For each row below, select the equivalent expression.
Select Option A, Option B, or neither option.
Row 1: Original = 4x^2 + 5 ; Option A = 8x^2 + 10 ; Option B = 4(x^2 + 5)
Row 2: Original = 6y − z ; Option A = 18y − 3z ; Option B = 12y − 6z
Row 3: Original = 4 ; Option A = 36x +9 / 9 ; Option B = 4x^2 + 12 / x^2 + 3

Answer 1

Row 1: neither
- Option A = 8x^2 + 10 = 2(4x^2 + 5), not equal to 4x^2 + 5.
- Option B = 4(x^2 + 5) = 4x^2 + 20, not equal.

Row 2: neither
- Option A = 18y − 3z = 3(6y − z), not equal.
- Option B = 12y − 6z, which is not equal to 6y − z (it does not simplify to the original).

Row 3: Option B
- Option B = (4x^2 + 12)/(x^2 + 3) = 4, since 4(x^2+3)/(x^2+3) = 4 (denominator ≠ 0 for real x).
- Option A does not simplify to 4.