What is the value of 4x 3+4x when x=4
The Correct Answer and Explanation is:
To solve the expression ( 4x^3 + 4x ) when ( x = 4 ), we can substitute the value of ( x ) into the equation.
- Substitute ( x = 4 ) into the equation:
[
4x^3 + 4x = 4(4^3) + 4(4)
] - Calculate the values:
- First, calculate ( 4^3 ), which means ( 4 \times 4 \times 4 ):
[
4^3 = 64
] - Now, substitute ( 64 ) back into the equation:
[
4(64) + 4(4)
] - Multiply:
[
4 \times 64 = 256
]
[
4 \times 4 = 16
]
- Add the results:
[
256 + 16 = 272
]
Thus, the value of the expression when ( x = 4 ) is ( 272 ).
Explanation
The expression ( 4x^3 + 4x ) contains two terms. The first term, ( 4x^3 ), involves the cube of ( x ), and the second term, ( 4x ), involves multiplying ( x ) by 4. When substituting ( x = 4 ), the cube of 4 is ( 64 ), and multiplying this by 4 gives ( 256 ). In the second term, multiplying ( 4 \times 4 ) gives ( 16 ). Adding these two results, we get ( 272 ).
This type of expression shows how the value of the variable ( x ) affects the overall value. The term ( x^3 ) grows rapidly as ( x ) increases, compared to the linear term ( 4x ). The larger the value of ( x ), the more dominant the cubic term becomes in determining the total value of the expression.
By performing the operations step by step—substituting ( x ), calculating powers, multiplying, and finally adding—you can simplify and solve complex algebraic expressions efficiently.