Question

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
36x +9 / 9

4x^2 + 12 / x^2 + 3

Answer 1

I’m not sure which specific question you want answered (e.g., “Which options are equal to the original?”, “Which are factored forms?”, etc.). I’ll cover the most likely interpretations — tell me which you meant or paste the exact problem text if I misread anything.

Assuming you want to know which options are equivalent (equal) to the Original for each row:

Row 1
- Original: 4x^2 + 5
- Option A: 8x^2 + 10 = 2(4x^2 + 5). This is a multiple of the original, but not equal (unless you allow multiplying both sides by 2).
- Option B: 4(x^2 + 5) = 4x^2 + 20, which is not equal to the original.
Conclusion: neither Option A nor B equals the original (A is 2× the original).

Row 2
- Original: 6y − z
- Option A: 18y − 3z = 3(6y − z) — a multiple of the original, not equal.
- Option B: 12y − 6z = 2(6y − z) — also a multiple, not equal.
Conclusion: neither option equals the original; both are scalar multiples (A = 3×, B = 2×).

Row 3
Your text is ambiguous, but one plausible reading is:
- Original: 4*(36x + 9)/9. Simplify: 36x + 9 = 9(4x+1), so 4*(36x+9)/9 = 4*(4x+1) = 16x + 4.
- Option (looks like): (4x^2 + 12)/(x^2 + 3). Simplify: factor numerator 4(x^2 + 3), cancel (x^2+3) to get 4.
Conclusion under this reading: the original simplifies to 16x + 4; the other expression simplifies to 4, so they are not equal (unless x satisfies 16x + 4 = 4, i.e. x = 0).

Tell me which exact question you need (e.g., “which options are equivalent?”, “which are factored forms?”, or “simplify each expression”), or paste the rows/options again on separate lines, and I’ll give the precise answers.