Addition, subtraction and multiplication of polynomials?

Question

1. (3x+2)+(-4x+3)

2. (6x+1)-(-7x+2)

3. -3x(x-1)

4. (x+5)(x-2)

5. (x-1)(x^2+x+1)

6. (-6x+2)+(x^2+x-3)

7. (3x^2-5x+4)-(x^2+8x-9)

8. -4x(2x^3-6x^2-5x+1)

9. (x-5)(2x-5)

10. (x+5)^2

Answer 1

Addition/subtraction: line up like terms, and add/subtract

example:

1.  (3x + 2) + (-4x + 3)

3x + 2 + -4x + 3

3x -4x + 2 + 3

-1x + 5

Multiplication:  multiply each term by the multiplier.  Remember the FOIL method:

First terms

Outer terms

Inner terms

Last terms

Examples:

3.  -3x*(x - 1)

-3x*(x - 1)

(-3x)*x + (-3x)*(-1)

-3(x^2) + 3x

9.  (x-5)(2x-5)

(x - 5)*(2x - 5)

x*2x + (-5)*(2x) + x*(-5) + (-5)*(-5)

2(x^2) - 10x - 5x + 25

2(x^2) - 15x + 25