Simplify the expression $x - 2 (1+x) + 3 (1-x) - 4 (1+2x) $.

Answer:see below

Step-by-step explanation:

1+x evaluates to 1+x

Multiply 2 by 1+x

we multiply 2 by each term in 1+x term by term.

This is the distributive property of multiplication.

Multiply 2 and 1

1

2 * 1 = 2

Multiply 2 and x

Multiply 1 and x

The x just gets copied along.

x

2 * x = 2x

2 * (1+x) evaluates to 2+2x

x - 2x = - x

The answer is - x-2

x-2 * (1+x) evaluates to - x-2

1-x evaluates to 1-x

Multiply 3 by 1-x

we multiply 3 by each term in 1-x term by term.

This is the distributive property of multiplication.

Multiply 3 and 1

1

3 * 1 = 3

Multiply 3 and - x

Multiply 1 and x

The x just gets copied along.

x

3 * - x = - 3x

3 * (1-x) evaluates to 3-3x

To add the polynomials - x-2 and 3-3x we try to add or combine terms in one polynomialwith any like terms in the other polynomial.

-x + - 3x = - 4x

-2 + 3 = 1

The answer is - 4x+1

x-2 * (1+x) + 3 * (1-x) evaluates to - 4x+1

Multiply x and 2

Multiply x and 1

The x just gets copied along.

The answer is x

x

2*x evaluates to 2x

1+2*x evaluates to 1+2x

Multiply 4 by 1+2x

we multiply 4 by each term in 1+2x term by term.

This is the distributive property of multiplication.

Multiply 4 and 1

1

4 * 1 = 4

Multiply 4 and 2x

Multiply 1 and x

The x just gets copied along.

x

4 * 2x = 8x

4 * (1+2*x) evaluates to 4+8x

To subtract the polynomials - 4x+1 and 4+8x we try to subtract terms in one polynomialwith any like terms in the other polynomial.

Be very careful with the "-" sign in front of 4+8x it is to be used on all terms in it.

-4x - 8x = - 12x

1 - 4 = - 3

The answer is - 12x-3

x-2 * (1+x) + 3 * (1-x) - 4 * (1+2*x) evaluates to - 12x-3

The final answer is

-12x-3