Answer:see below
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