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