Simplifying Polynomials

Question

Simplifying Polynomials:

 

a)     (x^2-1) - (x^2-x-1) =

 

b)     x^3(x+1) + x^5 (x^2-x) =

 

c)     x^4 (1-x^4) + x^8 (1-x^8) =

 

d)     (x+5) (x^2 +1) =

 

 those were not negatives

Answer 1

 -(x²-1)-(x²-x-1)

Distribute the negative through

the parenthesis

= -x²+1-x²+x+1

Combine like terms

= -2x²+x+2

 

b.  -x³(x+1) + x⁵(x²+x)

= -x³(x)-x³(1)+x⁵(x²)+x⁵(x)

= -x⁴-x³+x⁷+x⁶

There are no like terms since all the

exponents are different.  Put in order

from highest to lowest power.

= x⁷+x⁶-x⁴-x³

 

c.  -x⁴(1-x⁴) + x⁸(1-x⁸)

= -x⁴(1) -x⁴(-x⁴) + x⁸(1) + x⁸(-x⁸)

= -x⁴ + x⁸ + x⁸ - x¹⁶

Combine like terms and put in

descending order of power

= -x¹⁶+2x⁸-x⁴

 

d.  -(x+5)(x²+1)

= -[x(x²) + x(1) + 5(x² ) +5(1)]

= -(x³ + x + 5x² + 5)

= -(x³ + 5x² + x + 5)

= -x³ - 5x² - x - 5