Expand and simplify the following expression:[math: (5a+2)2−3a+9] (5a+2)^2-3a+9

Question

BlackTom AI · Accepted Answer

We start by expanding the squared binomial and then combine like terms step by step.
Option analysis begins by expanding (5a+2)^2: (5a+2)^2 = 25a^2 + 20a + 4.
Next, we subtract 3a: (25a^2 + 20a + 4) - 3a = 25a^2 + 17a + 4.
Finally, we add 9: (25a^2 + 17a + 4) + 9 = 25a^2 + 17a + 13.
Now evaluate each answer choice against this result.

Option a: 5a^2 + 23a + 13 (as given in the first part of the option) does not match the expanded form since the coefficient of a^2 is incorrect (5a^2 instead of 25a^2) and the linear term 23a does not align with 17a. This shows a miscalculation in the squared term or the combination process.

Option b: 25a^2 + 17a + 13 (the expanded form we calculated) has the correct a^2 coefficient, the correct a-term, and the constant term matches after including the +9. This aligns with the step-by-step expansion and combining like terms.

Option c: 25a^2 − 3a + 13 changes the linear term to −3a, which would correspond to omitting the +20a from the expansion of (5a+2)^2 and incorrectly applying the subsequent subtraction and addition. This contradicts the actual combination, so it is not correct.

Option d: 5a^2 + 17a + 13 again has an incorrect a^2 coefficient (5a^2 instead of 25a^2). The discrepancy in the squared term means this cannot be the correct simplification.

In summary, the only option whose coefficients match the correctly expanded and simplified expression 25a^2 + 17a + 13 is the one containing that exact polynomial form. The comparison shows that the expanded square contributes 25a^2 and 20a, then the linear and constant terms are adjusted by −3a and +9 to arrive at the final constant and linear terms.

Expand and simplify the following expression:[math: (5a+2)2−3a+9] (5a+2)^2-3a+9

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