High School

Which choice is equivalent to the expression below when \( y > 0 \)?

\[
\sqrt{y^3} + \sqrt{16^3} - 4y\sqrt{y}
\]

Answer :

The expression √y3 + √16^3 - 4y√y can be simplified using the formula (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3.

Let a = √y and b = 2√y. Then, we have:

√y3 + √16^3 - 4y√y
= √y^3 + (2√y)^3 + 3√y(2√y)^2
= (√y + 2√y)^3
= (3√y)^3
= 27y√y

Therefore, the equivalent choice for the expression √y3 + √16^3 - 4y√y when y >/ 0 is 27y√y.
To find the equivalent expression for √y^3 + √16^3 - 4y√y when y > 0, we need to simplify the given expression:

1. Simplify the cube root of 16^3: √16^3 = 16, because 16 * 16 * 16 = 16^3.
2. Simplify the last term: 4y√y = 4y * y^(1/2) = 4y^(3/2), because multiplying exponents with the same base, you add the exponents (1 + 1/2 = 3/2).

So, the equivalent expression is: √y^3 + 16 - 4y^(3/2).

To learn more about equivalent expression - brainly.com/question/28170201

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