Select the simplified form of this expression.
3x ^ 2 – 5y + 2x ^ 2 + 8y
Click on your answer below:
A. 6×4 – 40y2
B. 5×4 + 3y²
C. 5×2-3y
D. 5×2 + 3y
E. 6×2 – 40y
The correct answer and explanation is:
The correct answer is D. 5x² + 3y.
Explanation:
To simplify the expression 3×2−5y+2×2+8y3x^2 – 5y + 2x^2 + 8y, follow these steps:
- Group like terms:
- The terms involving x2x^2 are 3x23x^2 and 2x22x^2. These can be combined because they both involve x2x^2.
- The terms involving yy are −5y-5y and 8y8y. These can also be combined because they both involve yy.
- Combine the like terms:
- Combine the x2x^2-terms: 3×2+2×2=5x23x^2 + 2x^2 = 5x^2
- Combine the yy-terms: −5y+8y=3y-5y + 8y = 3y
- Write the simplified expression:
After combining like terms, the expression becomes: 5×2+3y5x^2 + 3y
Why other options are incorrect:
- A. 6x⁴ – 40y²: This answer incorrectly increases the powers of xx and yy, which isn’t supported by the original terms in the expression.
- B. 5x⁴ + 3y²: Again, this answer incorrectly increases the powers of both xx and yy, whereas the original powers are squared (x2x^2 and yy).
- C. 5x² – 3y: This answer incorrectly combines the yy-terms as −3y-3y instead of +3y+3y.
- E. 6x² – 40y: The coefficient of the x2x^2-term is incorrect, as it should be 5, not 6. Also, the yy-term is incorrectly combined.
Therefore, the correct simplified form is 5x² + 3y, which corresponds to answer D.