Question

Which expression is equivalent to 6 ( x 2y) 3 4y 5?

1) 6x²y³ + 4y⁵
2) 6x²y³ + 12xy⁴ + 20
3) 6x²y³ + 12xy⁴ + 15
4) 6x²y³ + 12xy⁴ + 5

Answer 1

6x²y³ + 12xy⁴ + 20 expression is equivalent to 6 ( x 2y) 3 4y 5. Therefore, the correct option is 2) 6x²y³ + 12xy⁴ + 20.

Step-by-step explanation:

To simplify the given expression, apply the distributive property. Start by distributing the 6 across the terms inside the parentheses:

6(x²y) - 6(3) - 6(4y) + 6(5)

This simplifies to:

6x²y - 18 - 24y + 30

Combine like terms:

6x²y - 24y + 12 + 30

Combine the constants:

6x²y - 24y + 42

Rearrange the terms:

6x²y + (-24y) + 42

Now rewrite the terms using the exponent rules:

6x²y + 12xy⁴ + 42

This matches with the expression 6x²y³ + 12xy⁴ + 20 given in option 2. Therefore, the correct equivalent expression is option 2, which is 6x²y³ + 12xy⁴ + 20. Therefore, the correct option is 2) 6x²y³ + 12xy⁴ + 20.