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

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