Question

Use the definitions and theorems of this section to evaluate and simplify the following expression. Be sure to express answers with positive exponents.

Answer 1

The Answer Is B13 or you can put it as B^13x

Answer 2

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

Explanation:

b^5 +b^8 =

You can easily solve this equation by doing factoring (a fancy word for dividing)

so, factor out the Greatest Common Factor (GCF)

which is

B^5

so in parenthesis write (1+b^3) next to it, think of subtracting the two exponents, and then since theres only 1 thing left after factoring out b^5, you leave a 1 behind.

b^5(1+b^3)

from here, in the parenthesis, you have 2 perfect cubes, 1 and b^3

take the cube root of that which is (1+b)

then use (a+b) which is already done

AND (a^2-ab+b^2) where a is equal to 1, and b is equal to variable b.

so, that would be

x^5(1+x)(1-1x+x^2) ( this is what you should get once you do multiply the square root out to just get constants and coefficients.

That gives us our final answer of x^5(1+x)(1-1x+x^2) because it is in the simplest form possible.