Final answer:
All four provided equations a. -3y⁴(5y² + 2) = -15y⁶ - 6y⁴, b. -7x²(4x³ + 2) = -28x⁵ - 14x², c. -2b³(6b² + 5) = -12b⁵ - 10b³ and d. -5d³(3d² + 4) = -15d⁵ - 20d³ are correct once the operation is performed on the left side.
Step-by-step explanation:
In Mathematics, the correctness of equations can be determined by comparing the left and right sides after performing the relevant operations. Let's consider the four equations you've provided:
a. -3y⁴(5y² + 2) = -15y⁶ - 6y⁴, b. -7x²(4x³ + 2) = -28x⁵ - 14x², c. -2b³(6b² + 5) = -12b⁵ - 10b³, d. -5d³(3d² + 4) = -15d⁵ - 20d³
For equation a, if we distribute -3y⁴ to (5y² + 2), we indeed get -15y⁶ - 6y⁴. So, equation a is correct. Looking at equation b, if we distribute -7x² to (4x³ + 2), we obtain -28x⁵ - 14x². Therefore, equation b too is correctly formed.
Proceeding with c, after distributing -2b³ to (6b² + 5), it results in -12b⁵ - 10b³. Hence, equation c is also accurate. Lastly, taking a look at equation d, upon distribution of -5d³ to (3d² + 4), it renders -15d⁵ - 20d³ which verifies that equation d is also correct.
Thus, all of the provided equations, a, b, c, and d, are correct.
Learn more about Distributive property in Mathematics