Answer:To simplify the expression 4x(x+1)-(3x-8)(x+4), we need to follow the distributive property and combine like terms.
Step 1: Distribute 4x to (x+1):
4x(x+1) = 4x^2 + 4x
Step 2: Distribute (3x-8) to (x+4):
(3x-8)(x+4) = 3x(x+4) - 8(x+4) = 3x^2 + 12x - 8x - 32 = 3x^2 + 4x - 32
Step 3: Subtract (3x^2 + 4x - 32) from (4x^2 + 4x):
4x^2 + 4x - (3x^2 + 4x - 32) = 4x^2 + 4x - 3x^2 - 4x + 32 = x^2 + 32
The resulting simplified expression is x^2 + 32.
In terms of classification, the resulting polynomial is a quadratic polynomial because it is in the form of ax^2 + bx + c, where a=1, b=0, and c=32.
Step-by-step explanation:
