Question
Which expression is equivalent to the given trinomial?
(1 point)
Responses
4x(4x+5x)
4 x open paren 4 x plus 5 x close paren
(2x2+4)(2x2−3)
open paren 2 x squared plus 4 close paren times open paren 2 x squared minus 3 close paren
(2x2+4)(2x2+3)
open paren 2 x squared plus 4 close paren times open paren 2 x squared plus 3 close paren
4x(x2+2x+3)
(1 point)
Responses
4x(4x+5x)
4 x open paren 4 x plus 5 x close paren
(2x2+4)(2x2−3)
open paren 2 x squared plus 4 close paren times open paren 2 x squared minus 3 close paren
(2x2+4)(2x2+3)
open paren 2 x squared plus 4 close paren times open paren 2 x squared plus 3 close paren
4x(x2+2x+3)
Answers
GPT-4o mini
To determine which expression is equivalent to the given trinomial, let's analyze each option one by one:
1. **4x(4x + 5x)**: This simplifies to \(4x \cdot 9x = 36x^2\).
2. **(2x^2 + 4)(2x^2 - 3)**: We can apply the distributive property (FOIL) to expand this expression:
\[
(2x^2 + 4)(2x^2 - 3) = 2x^2 \cdot 2x^2 + 2x^2 \cdot (-3) + 4 \cdot 2x^2 + 4 \cdot (-3) = 4x^4 - 6x^2 + 8x^2 - 12 = 4x^4 + 2x^2 - 12.
\]
3. **(2x^2 + 4)(2x^2 + 3)**: Again applying the distributive property:
\[
(2x^2 + 4)(2x^2 + 3) = 2x^2 \cdot 2x^2 + 2x^2 \cdot 3 + 4 \cdot 2x^2 + 4 \cdot 3 = 4x^4 + 6x^2 + 8x^2 + 12 = 4x^4 + 14x^2 + 12.
\]
4. **4x(x^2 + 2x + 3)**: Using the distributive property once more,
\[
4x(x^2 + 2x + 3) = 4x^3 + 8x^2 + 12x.
\]
Without knowing the specific trinomial we are trying to match with these expressions, let's summarize the findings:
- \(4x(4x + 5x) = 36x^2\)
- \((2x^2 + 4)(2x^2 - 3) = 4x^4 + 2x^2 - 12\)
- \((2x^2 + 4)(2x^2 + 3) = 4x^4 + 14x^2 + 12\)
- \(4x(x^2 + 2x + 3) = 4x^3 + 8x^2 + 12x\)
From these expansions, we see that none of these directly match a standard trinomial form (\(ax^2 + bx + c\)). To identify the best option, we would need the specific trinomial that was originally provided. However, among the answers provided and depending on that context, one of the expressions might align closely, but as listed they do not equate to a typical trinomial \(ax^2 + bx + c\).
Please provide the original trinomial for precise identification.
1. **4x(4x + 5x)**: This simplifies to \(4x \cdot 9x = 36x^2\).
2. **(2x^2 + 4)(2x^2 - 3)**: We can apply the distributive property (FOIL) to expand this expression:
\[
(2x^2 + 4)(2x^2 - 3) = 2x^2 \cdot 2x^2 + 2x^2 \cdot (-3) + 4 \cdot 2x^2 + 4 \cdot (-3) = 4x^4 - 6x^2 + 8x^2 - 12 = 4x^4 + 2x^2 - 12.
\]
3. **(2x^2 + 4)(2x^2 + 3)**: Again applying the distributive property:
\[
(2x^2 + 4)(2x^2 + 3) = 2x^2 \cdot 2x^2 + 2x^2 \cdot 3 + 4 \cdot 2x^2 + 4 \cdot 3 = 4x^4 + 6x^2 + 8x^2 + 12 = 4x^4 + 14x^2 + 12.
\]
4. **4x(x^2 + 2x + 3)**: Using the distributive property once more,
\[
4x(x^2 + 2x + 3) = 4x^3 + 8x^2 + 12x.
\]
Without knowing the specific trinomial we are trying to match with these expressions, let's summarize the findings:
- \(4x(4x + 5x) = 36x^2\)
- \((2x^2 + 4)(2x^2 - 3) = 4x^4 + 2x^2 - 12\)
- \((2x^2 + 4)(2x^2 + 3) = 4x^4 + 14x^2 + 12\)
- \(4x(x^2 + 2x + 3) = 4x^3 + 8x^2 + 12x\)
From these expansions, we see that none of these directly match a standard trinomial form (\(ax^2 + bx + c\)). To identify the best option, we would need the specific trinomial that was originally provided. However, among the answers provided and depending on that context, one of the expressions might align closely, but as listed they do not equate to a typical trinomial \(ax^2 + bx + c\).
Please provide the original trinomial for precise identification.