(5-2x)(4x%2B1).jpeg "(2/3x-4)(5-2x)(4x+1)")
Expanding and Simplifying the Expression (2/3x-4)(5-2x)(4x+1)
This article will guide you through the process of expanding and simplifying the given expression: (2/3x-4)(5-2x)(4x+1).
Step 1: Expand the first two factors
We will start by multiplying the first two factors: (2/3x-4) and (5-2x).
(2/3x-4)(5-2x) = (2/3x * 5) + (2/3x * -2x) + (-4 * 5) + (-4 * -2x)
Simplifying the terms:
= 10/3x - 4/3x^2 - 20 + 8x
Step 2: Combine like terms
Combine the x and x^2 terms:
= -4/3x^2 + (10/3 + 8)x - 20
Simplify the coefficient of the x term:
= -4/3x^2 + 34/3x - 20
Step 3: Multiply the result by the third factor
Now, we multiply the simplified result from Step 2 by the third factor (4x+1):
(-4/3x^2 + 34/3x - 20) (4x+1)
Expanding the product:
= (-4/3x^2 * 4x) + (-4/3x^2 * 1) + (34/3x * 4x) + (34/3x * 1) + (-20 * 4x) + (-20 * 1)
Simplifying the terms:
= -16/3x^3 - 4/3x^2 + 136/3x^2 + 34/3x - 80x - 20
Step 4: Combine like terms
Combine the x^2, x, and constant terms:
= -16/3x^3 + (136/3 - 4/3)x^2 + (34/3 - 80)x - 20
Simplify the coefficients:
= -16/3x^3 + 132/3x^2 - 226/3x - 20
Final Simplified Expression
The fully expanded and simplified form of the expression (2/3x-4)(5-2x)(4x+1) is:
-16/3x^3 + 132/3x^2 - 226/3x - 20