Simplify each expression (y^2 )( 2y)
*
2y
2y^3
-2y^3
-2y
The simplified expression is 2y^3.
To simplify each expression, we will use the properties of exponents.
1. (y^2) * (2y):
Multiply the coefficients: 2 * 1 = 2.
Add the exponents of y: y^2 * y = y^(2+1) = y^3.
Therefore, the simplified expression is 2y^3.
2. 2y * 2y^3:
Multiply the coefficients: 2 * 2 = 4.
Add the exponents of y: y * y^3 = y^(1+3) = y^4.
Therefore, the simplified expression is 4y^4.
3. (-2y) * (-2y^3):
Multiply the coefficients: -2 * -2 = 4.
Since we are multiplying negative numbers, the result is positive.
Add the exponents of y: y * y^3 = y^(1+3) = y^4.
Therefore, the simplified expression is 4y^4.
4. (-2y) * 2y:
Multiply the coefficients: -2 * 2 = -4.
Multiply the variables: y * y = y^2.
Therefore, the simplified expression is -4y^2.