Simplify the expressions. Show your work. 1.(3x(4x4 – 5x)2.(5x4 – 3x3 + 6x) – ( 3x3 + 11x2 – 8x) 3. (x – 2) (3x-4) 4.(x + 6)2

1. (3x(4x^4 - 5x))
    Steps
Distributive Formula: a(b + c) = ab + ac
a = 3x
b = 4x^4 
c = -5x
= 3x * 4x^4 + 3x(-5x)
= 3x * 4x^4 - 3x * 5x
Simplify,
= 12x^5 - 15x^2


2. (5x^4 - 3x^3 + 6x) - (3x^3 + 11x^2 - 8x)
    Steps
Remove the parentheses: (a) = a
= 5x^4 - 3x^3 + 6x - (3x^3 + 11x^2 - 8x)
-(3x^3 + 11x^2 - 8x): -3x^3 - 11x^2 + 8x
= 5x^4 - 3x^3 + 6x - 3x^3 - 11x^2 + 8x
Then simplify,
= 5x^4 - 6x^3 - 11x^2 + 14x


3. (x - 2)(3x - 4)
    Steps
Distributive formula: (a + b)(c + d) = ac + ad + bc + bd
a = x
b = -2
c = 3x
d = -4
= x * 3x + x(-4) - 2 * 3x - 2(-4)
= x * 3x - x * 4 - 2 * 3x + 2 * 4
Then simplify,
= 3x^2 - 10x + 8


4. (x + 6)^2
    Steps
Formula: (a + b)^2 = a^2 + 2ab + b^2
a = x
b = 6
= x^2 + 2x * 6 + 6^2
Simplify,
= x^2 + 12x + 36