The expression 2x^3(4-3x)-5x(x-2) is equal to?
*Please show me the steps to solve this problem! Thanks!
Use the distributive rule of algebra. This is not geometry.
2X^3(4 - 3X) -5X(X - 2).
2X^3*4 + 2X^3(-3X) -SX*X -5X*(-2) =
8X^3 - 6X^4 -5X^2 + 10X =
Arrange exponents in decreasing order:
-6X^4 + 8X^3 -5X^2 + 10X.
The question is not about trigonometry.
To simplify the expression 2x^3(4-3x) - 5x(x-2), we will follow the order of operations (PEMDAS) to evaluate each part of the expression:
Step 1: Distribute the 2x^3 to the terms inside the parentheses (4-3x):
2x^3 * 4 = 8x^3
2x^3 * (-3x) = -6x^4
So the expression becomes 8x^3 - 6x^4.
Step 2: Distribute the -5x to the terms inside the parentheses (x-2):
-5x * x = -5x^2
-5x * (-2) = 10x
So the expression becomes 8x^3 - 6x^4 - 5x^2 + 10x.
Now we can simplify further by combining like terms:
Step 3: Combine the x^3 terms:
8x^3 - 6x^4 remains the same.
Step 4: Combine the x^2 terms:
-5x^2 remains the same.
Step 5: Combine the x terms:
10x remains the same.
Therefore, the simplified form of the expression 2x^3(4-3x) - 5x(x-2) is:
8x^3 - 6x^4 - 5x^2 + 10x.